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Abraham Adrian Albert 1905-1972. (English) Zbl 0292.01025


MSC:

01A70 Biographies, obituaries, personalia, bibliographies

Biographic References:

Albert, Abraham Adrian
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[1] Abraham Adrian Albert, Modern Higher Algebra, Univ. of Chicago Press, Chicago, Ill., 1937. · Zbl 0017.29201
[2] A. Adrian Albert, Structure of algebras, Revised printing. American Mathematical Society Colloquium Publications, Vol. XXIV, American Mathematical Society, Providence, R.I., 1961.
[3] A. Adrian Albert, Introduction to Algebraic Theories, University of Chicago Press, Chicago, 1941. · Zbl 0027.00601
[4] Abraham Adrian Albert, College Algebra, McGraw-Hill, New York, 1946; reprinted by Univ. of Chicago Press, Chicago, Ill., 1963.
[5] Abraham Adrian Albert, Solid Analytic Geometry, McGraw-Hill, New York, 1949. · Zbl 0039.16006
[6] A. Adrian Albert, Fundamental concepts of higher algebra, The University of Chicago Press, Chicago, Ill., 1958. · Zbl 0092.04001
[7] A. Adrian Albert and Reuben Sandler, An introduction to finite projective planes, Holt, Rinehart and Winston, New York-Toronto, Ont.-London, 1968. · Zbl 0194.21502
[8] Studies in modern algebra, Studies in Mathematics, Vol. 2, Published by The Mathematical Association of America; distributed by Prentice-Hall, Inc., Englewood Cliffs, N.J., 1963. · Zbl 0192.00102
[9] Abraham Adrian Albert, A determination of all associative algebras in two, three and four units over a nonmodular field F, M.S. Thesis, University of Chicago, Chicago, Ill., 1927.
[10] Abraham Adrian Albert, Algebras and their radicals, and division algebras, Ph.D. Dissertation, University of Chicago, Chicago, Ill., 1928.
[11] A. Adrian Albert, A determination of all normal division algebras in sixteen units, Trans. Amer. Math. Soc. 31 (1929), no. 2, 253 – 260. · JFM 55.0090.04
[12] Abraham Adrian Albert, On the rank equation of any normal division algebra, Bull. Amer. Math. Soc. 35 (1929), 335-338. · JFM 55.0090.03
[13] Abraham Adrian Albert, The rank function of any simple algebra, Proc. Nat. Acad. Sci. U.S.A. 15 (1929), 372-376. · JFM 55.0683.03
[14] Abraham Adrian Albert, On the structure of normal division algebras, Ann. of Math. 30 (1929), 322-338. · JFM 55.0682.01
[15] Abraham Adrian Albert, Normal division algebras in 4p2 units, p an odd prime, Ann. of Math. 30 (1929), 583-590. · JFM 55.0683.01
[16] Abraham Adrian Albert, The structure of an algebra which is a direct product of rational generalized quaternion division algebras, Ann. of Math. 30 (1929), 621-625. · JFM 55.0683.02
[17] Abraham Adrian Albert, On the structure of pure Riemann matrices with non-commutative multiplication algebras, Proc. Nat. Acad. Sci. U.S.A. 16 (1930), 308-312. · JFM 56.0329.08
[18] Abraham Adrian Albert, On direct products, cyclic division algebras, and pure Riemann matrices, Proc. Nat. Acad. Sci. U.S.A. 16 (1930), 313-315. · JFM 56.0869.01
[19] A. Adrian Albert, The non-existence of pure Riemann matrices with normal multiplication algebras of order sixteen, Ann. of Math. (2) 31 (1930), no. 3, 375 – 380. · JFM 56.0869.02 · doi:10.2307/1968233
[20] Abraham Adrian Albert, A necessary and sufficient condition for the non-equivalence of any two rational generalized quaternion division algebras, Bull. Amer. Math. Soc. 36 (1930), 535-540. · JFM 56.0145.03
[21] A. Adrian Albert, Determination of All Normal Division Algebras in Thirty-Six Units of Type R\(_{2}\), Amer. J. Math. 52 (1930), no. 2, 283 – 292. · JFM 56.0145.06 · doi:10.2307/2370683
[22] Abraham Adrian Albert, A note on an important theorem on normal division algebras, Bull. Amer. Math. Soc. 36 (1930), 649-650. · JFM 56.0145.04
[23] A. Adrian Albert, New results in the theory of normal division algebras, Trans. Amer. Math. Soc. 32 (1930), no. 2, 171 – 195. · JFM 56.0146.01
[24] A. Adrian Albert, The integers of normal quartic fields, Ann. of Math. (2) 31 (1930), no. 3, 381 – 418. · JFM 56.0870.02 · doi:10.2307/1968234
[25] A. Adrian Albert, A determination of the integers of all cubic fields, Ann. of Math. (2) 31 (1930), no. 4, 550 – 566. · JFM 56.0870.01 · doi:10.2307/1968153
[26] A. Adrian Albert, A construction of all non-commutative rational division algebras of order eight, Ann. of Math. (2) 31 (1930), no. 4, 567 – 576. · JFM 56.0145.05 · doi:10.2307/1968154
[27] Abraham Adrian Albert, Normal division algebras of order 22m, Proc. Nat. Acad. Sci. U.S.A. 17 (1931), 389-392. · Zbl 0002.11502
[28] Abraham Adrian Albert, The structure of pure Riemann matrices with noncommutative multiplication algebras, Palermo Rendiconti 55 (1931), 57-115. · JFM 57.0161.03
[29] A. Adrian Albert, On direct products, cyclic division algebras, and pure Riemann matrices, Trans. Amer. Math. Soc. 33 (1931), no. 1, 219 – 234. · Zbl 0001.11602
[30] A. Adrian Albert, On normal division algebras of type \? in thirty-six units, Trans. Amer. Math. Soc. 33 (1931), no. 1, 235 – 243. · Zbl 0001.11701
[31] Abraham Adrian Albert, On the Wedderburn norm condition for cyclic algebras, Bull. Amer. Math. Soc. 37 (1931), 301-312. · Zbl 0001.26701
[32] Abraham Adrian Albert, A note on cyclic algebras of order 16, Bull. Amer. Math. Soc. 37 (1931), 727-730. · Zbl 0003.05302
[33] A. Adrian Albert, On direct products, Trans. Amer. Math. Soc. 33 (1931), no. 3, 690 – 711. · Zbl 0002.24605
[34] Abraham Adrian Albert, Division algebras over an algebraic field, Bull. Amer. Math. Soc. 37 (1931), 777-784. · Zbl 0003.05303
[35] A. Adrian Albert, The structure of matrices with any normal division algebra of multiplications, Ann. of Math. (2) 32 (1931), no. 1, 131 – 148. · Zbl 0001.26603 · doi:10.2307/1968420
[36] A. Adrian Albert, On the Construction of Cyclic Algebras with a Given Exponent, Amer. J. Math. 54 (1932), no. 1, 1 – 13. · Zbl 0003.24405 · doi:10.2307/2371072
[37] A. Adrian Albert, Algebras of degree 2^{\?} and pure Riemann matrices, Ann. of Math. (2) 33 (1932), no. 2, 311 – 318. · Zbl 0004.10001 · doi:10.2307/1968332
[38] Abraham Adrian Albert, A construction of non-cyclic normal division algebras, Bull. Amer. Math. Soc. 38 (1932), 449-456. · Zbl 0005.00603
[39] A. Adrian Albert, Normal division algebras of degree four over an algebraic field, Trans. Amer. Math. Soc. 34 (1932), no. 2, 363 – 372. · Zbl 0004.10002
[40] A. Adrian Albert, On normal simple algebras, Trans. Amer. Math. Soc. 34 (1932), no. 3, 620 – 625. · Zbl 0005.05002
[41] Abraham Adrian Albert, A note on division algebras of order sixteen, Bull. Amer. Math. Soc. 38 (1932), 703-706. · Zbl 0005.34202
[42] A. Adrian Albert and Helmut Hasse, A determination of all normal division algebras over an algebraic number field, Trans. Amer. Math. Soc. 34 (1932), no. 3, 722 – 726. · Zbl 0005.05003
[43] Abraham Adrian Albert, A note on the equivalence of algebras of degree two, Bull. Amer. Math. Soc. 39 (1933), 257-258. · Zbl 0007.05502
[44] Abraham Adrian Albert, On primary normal division algebras of degree eight, Bull. Amer. Math. Soc. 39 (1933), 265-272. · Zbl 0007.05503
[45] A. Adrian Albert, Non-cyclic algebras of degree and exponent four, Trans. Amer. Math. Soc. 35 (1933), no. 1, 112 – 121. · Zbl 0006.15103
[46] A. Adrian Albert, The Integers Represented by Sets of Ternary Quadratic Forms, Amer. J. Math. 55 (1933), no. 1-4, 274 – 292. · Zbl 0006.29004 · doi:10.2307/2371130
[47] A. Adrian Albert, On universal sets of positive ternary quadratic forms, Ann. of Math. (2) 34 (1933), no. 4, 875 – 878. · Zbl 0007.39204 · doi:10.2307/1968705
[48] Abraham Adrian Albert, A note on the Dickson theorem on universal ternaries, Bull. Amer. Math. Soc. 39 (1933), 585-588. · Zbl 0007.33704
[49] Abraham Adrian Albert, Normal division algebras over algebraic number fields not of finite degree, Bull. Amer. Math. Soc. 39 (1933), 746-749. · Zbl 0008.00104
[50] A. Adrian Albert, Cyclic fields of degree eight, Trans. Amer. Math. Soc. 35 (1933), no. 4, 949 – 964. · Zbl 0008.00201
[51] A. Adrian Albert, On the construction of Riemann matrices. I, Ann. of Math. (2) 35 (1934), no. 1, 1 – 28. · Zbl 0010.00304 · doi:10.2307/1968116
[52] A. Adrian Albert, On a certain algebra of quantum mechanics, Ann. of Math. (2) 35 (1934), no. 1, 65 – 73. · Zbl 0008.42104 · doi:10.2307/1968118
[53] Abraham Adrian Albert, Normal division algebras of degree 4 over F of characteristic 2, Amer. J. Math. 56 (1934), 75-86. · Zbl 0008.24202
[54] Abraham Adrian Albert, Integral domains of rational generalized quaternion algebras, Bull. Amer. Soc. 40 (1934), 164-176. · Zbl 0008.29301
[55] A. Adrian Albert, On certain imprimitive fields of degree \?² over \? of characteristic \?, Ann. of Math. (2) 35 (1934), no. 2, 211 – 219. · Zbl 0009.24302 · doi:10.2307/1968426
[56] A. Adrian Albert, Normal division algebras over a modular field, Trans. Amer. Math. Soc. 36 (1934), no. 2, 388 – 394. · Zbl 0009.19502
[57] A. Adrian Albert, A solution of the principal problem in the theory of Riemann matrices, Ann. of Math. (2) 35 (1934), no. 3, 500 – 515. · Zbl 0010.00401 · doi:10.2307/1968747
[58] Abraham Adrian Albert, Cyclic fields of degree p, Bull. Amer. Math. Soc. 40 (1934), 625-631. · Zbl 0010.00402
[59] A. Adrian Albert, On normal Kummer fields over a non-modular field, Trans. Amer. Math. Soc. 36 (1934), no. 4, 885 – 892. · Zbl 0010.14902
[60] Abraham Adrian Albert, Involutorial simple algebras and real Riemann matrices, Proc. Nat. Acad. Sci. U.S.A. 20 (1934), 676-681. · Zbl 0010.29203
[61] Abraham Adrian Albert, The principal matrices of a Riemann matrix, Bull. Amer. Math. Soc. 40 (1934), 843-846. · Zbl 0010.29202
[62] A. Adrian Albert, A note on the Poincaré theorem on impure Riemann matrices, Ann. of Math. (2) 36 (1935), no. 1, 151 – 156. · Zbl 0011.00603 · doi:10.2307/1968670
[63] A. Adrian Albert, On the construction of Riemann matrices. II, Ann. of Math. (2) 36 (1935), no. 2, 376 – 394. · Zbl 0011.38904 · doi:10.2307/1968578
[64] A. Adrian Albert, On cyclic fields, Trans. Amer. Math. Soc. 37 (1935), no. 3, 454 – 462. · Zbl 0011.29005
[65] A. Adrian Albert, Involutorial simple algebras and real Riemann matrices, Ann. of Math. (2) 36 (1935), no. 4, 886 – 964. · Zbl 0012.39102 · doi:10.2307/1968595
[66] A. Adrian Albert, Normal division algebras of degree \?^{\?} over \? of characteristic \?, Trans. Amer. Math. Soc. 39 (1936), no. 1, 183 – 188. · Zbl 0013.10202
[67] A. Adrian Albert, Simple algebras of degree \?^{\?} over a centrum of characteristic \?, Trans. Amer. Math. Soc. 40 (1936), no. 1, 112 – 126. · Zbl 0014.29102
[68] Irving Kaplansky, Abraham Adrian Albert. November 9, 1905 – June 6, 1972, A century of mathematics in America, Part I, Hist. Math., vol. 1, Amer. Math. Soc., Providence, RI, 1988, pp. 244 – 264.
[69] Abraham Adrian Albert, p-algebras over a field generated by one indeterminate, Bull. Amer. Math. Soc. 43 (1937), 733-736. · Zbl 0017.24501
[70] A. Adrian Albert, Normalized integral bases of algebraic number fields. I, Ann. of Math. (2) 38 (1937), no. 4, 923 – 957. · Zbl 0018.05102 · doi:10.2307/1968847
[71] Abraham Adrian Albert, A quadratic form problem in the calculus of variations, Bull. Amer. Math. Soc. 44 (1938), 250-253. · Zbl 0018.24201
[72] Abraham Adrian Albert, Non-cyclic algebras with pure maximal subfields, Bull. Amer. Math Soc. 44 (1938), 576-579. · Zbl 0019.19302
[73] A. Adrian Albert, Symmetric and alternate matrices in an arbitrary field. I, Trans. Amer. Math. Soc. 43 (1938), no. 3, 386 – 436. · Zbl 0018.34202
[74] A. Adrian Albert, Quadratic null forms over a function field, Ann. of Math. (2) 39 (1938), no. 2, 494 – 505. · Zbl 0019.00207 · doi:10.2307/1968799
[75] A. Adrian Albert, On cyclic algebras, Ann. of Math. (2) 39 (1938), no. 3, 669 – 682. · Zbl 0019.24601 · doi:10.2307/1968641
[76] Abraham Adrian Albert, A note on normal division algebras of prime degree, Bull. Amer. Math. Soc. 44 (1938), 649-652. · Zbl 0019.29002
[77] A. A. Albert, On ordered algebras, Bull. Amer. Math. Soc. 46 (1940), 521 – 522. · Zbl 0061.05502
[78] A. A. Albert, On \?-adic fields and rational division algebras, Ann. of Math. (2) 41 (1940), 674 – 693. · Zbl 0024.14602 · doi:10.2307/1968740
[79] A. A. Albert, A rule for computing the inverse of a matrix, Amer. Math. Monthly 48 (1941), 198 – 199. · Zbl 0060.03301 · doi:10.2307/2304250
[80] A. A. Albert, Division algebras over a function field, Duke Math. J. 8 (1941), 750 – 762. · Zbl 0061.05503
[81] A. A. Albert, Quadratic forms permitting composition, Ann. of Math. (2) 43 (1942), 161 – 177. · Zbl 0060.04003 · doi:10.2307/1968887
[82] A. A. Albert, Non-associative algebras. I. Fundamental concepts and isotopy, Ann. of Math. (2) 43 (1942), 685 – 707. · Zbl 0061.04807 · doi:10.2307/1968960
[83] A. A. Albert, Non-associative algebras. II. New simple algebras, Ann. of Math. (2) 43 (1942), 708 – 723. · Zbl 0061.04901 · doi:10.2307/1968961
[84] A. A. Albert, The radical of a non-associative algebra, Bull. Amer. Math. Soc. 48 (1942), 891 – 897. · Zbl 0061.05001
[85] A. A. Albert, An inductive proof of Descartes’ rule of signs, Amer. Math. Monthly 50 (1943), 178 – 180. · Zbl 0060.05004 · doi:10.2307/2302399
[86] A. A. Albert, Discussions and Notes: A Suggestion for a Simplified Trigonometry, Amer. Math. Monthly 50 (1943), no. 4, 251 – 253. · doi:10.2307/2303930
[87] A. A. Albert, Quasigroups. I, Trans. Amer. Math. Soc. 54 (1943), 507 – 519. · Zbl 0063.00039
[88] A. A. Albert, Algebras derived by non-associative matrix multiplication, Amer. J. Math. 66 (1944), 30 – 40. · Zbl 0061.05003 · doi:10.2307/2371893
[89] A. A. Albert, The matrices of factor analysis, Proc. Nat. Acad. Sci. U. S. A. 30 (1944), 90 – 95. · Zbl 0063.00040
[90] A. A. Albert, The minimum rank of a correlation matrix, Proc. Nat. Acad. Sci. U. S. A. 30 (1944), 144 – 146. · Zbl 0063.00041
[91] A. A. Albert, Quasigroups. II, Trans. Amer. Math. Soc. 55 (1944), 401 – 419. · Zbl 0063.00042
[92] A. A. Albert, Two element generation of a separable algebra, Bull. Amer. Math. Soc. 50 (1944), 786 – 788. · Zbl 0061.05501
[93] Abraham Adrian Albert, Quasiquaternion algebras, Ann. of Math. (2) 45 (1944), 623-638. MR 6, 115. · Zbl 0061.05002
[94] A. A. Albert, On Jordan algebras of linear transformations, Trans. Amer. Math. Soc. 59 (1946), 524 – 555. · Zbl 0061.05101
[95] A. A. Albert, The Wedderburn principal theorem for Jordan algebras, Ann. of Math. (2) 48 (1947), 1 – 7. · Zbl 0029.01002 · doi:10.2307/1969210
[96] A. A. Albert, Absolute valued real algebras, Ann. of Math. (2) 48 (1947), 495 – 501. · Zbl 0029.01001 · doi:10.2307/1969182
[97] A. A. Albert, A structure theory for Jordan algebras, Ann. of Math. (2) 48 (1947), 546 – 567. · Zbl 0029.01003 · doi:10.2307/1969128
[98] A. A. Albert, On the power-associativity of rings, Summa Brasil. Math. 2 (1948), no. 2, 21 – 32.
[99] A. A. Albert, Power-associative rings, Trans. Amer. Math. Soc. 64 (1948), 552 – 593. · Zbl 0033.15402
[100] A. A. Albert, On the right alternative algebras, Ann. of Math. (2) 50 (1949), 318 – 328. · Zbl 0033.15501 · doi:10.2307/1969457
[101] A. A. Albert, Absolute-valued algebraic algebras, Bull. Amer. Math. Soc. 55 (1949), 763 – 768. · Zbl 0033.34901
[102] A. A. Albert, A theory of trace-admissible algebras, Proc. Nat. Acad. Sci. U. S. A. 35 (1949), 317 – 322. · Zbl 0033.15403
[103] A. A. Albert, Almost alternative algebras, Portugaliae Math. 8 (1949), 23 – 36. · Zbl 0033.15401
[104] A. A. Albert, A note on the exceptional Jordan algebra, Proc. Nat. Acad. Sci. U. S. A. 36 (1950), 372 – 374. · Zbl 0037.15904
[105] A. A. Albert, A theory of power-associative commutative algebras, Trans. Amer. Math. Soc. 69 (1950), 503 – 527. · Zbl 0039.26501
[106] A. A. Albert, New simple power-associative algebras, Summa Brasil. Math. 2 (1951), 183 – 194. · Zbl 0045.32101
[107] A. A. Albert, Power-associative algebras, Proceedings of the International Congress of Mathematicians, Cambridge, Mass., 1950, vol. 2, Amer. Math. Soc., Providence, R. I., 1952, pp. 25 – 32.
[108] A. A. Albert, On nonassociative division algebras, Trans. Amer. Math. Soc. 72 (1952), 296 – 309. · Zbl 0046.03601
[109] A. A. Albert, On simple alternative rings, Canadian J. Math. 4 (1952), 129 – 135. · Zbl 0046.25403
[110] A. A. Albert, On commutative power-associative algebras of degree two, Trans. Amer. Math. Soc. 74 (1953), 323 – 343. · Zbl 0051.02302
[111] A. A. Albert, Rational normal matrices satisfying the incidence equation, Proc. Amer. Math. Soc. 4 (1953), 554 – 559. · Zbl 0050.01004
[112] A. A. Albert, The structure of right alternative algebras, Ann. of Math. (2) 59 (1954), 408 – 417. · Zbl 0055.26501 · doi:10.2307/1969709
[113] A. A. Albert and M. S. Frank, Simple Lie algebras of characteristic \?, Univ. e Politec. Torino. Rend. Sem. Mat. 14 (1954 – 55), 117 – 139.
[114] A. A. Albert, Leonard Eugene Dickson, 1874 – 1954, Bull. Amer. Math. Soc. 61 (1955), 331 – 345. · Zbl 0065.24408
[115] A. A. Albert, On involutorial algebras, Proc. Nat. Acad. Sci. U.S.A. 41 (1955), 480 – 482. · Zbl 0064.27201
[116] A. A. Albert, On Hermitian operators over the Cayley algebra, Proc. Nat. Acad. Sci. U. S. A. 41 (1955), 639 – 640. · Zbl 0065.02002
[117] A. A. Albert, A property of special Jordan algebras, Proc. Nat. Acad. Sci. U.S.A. 42 (1956), 624 – 625. · Zbl 0071.25803
[118] A. A. Albert, The norm form of a rational division algebra, Proc. Nat. Acad. Sci. U.S.A. 43 (1957), 506 – 509. · Zbl 0078.02602
[119] A. A. Albert, On certain trinomial equations in finite fields, Ann. of Math. (2) 66 (1957), 170 – 178. · Zbl 0082.03702 · doi:10.2307/1970123
[120] Abraham Adrian Albert, (with B. Muckenhoupt), On matrices of trace zero, Michigan Math. J. 4 (1957), 1-3. MR 18, 786.
[121] A. A. Albert, On partially stable algebras, Trans. Amer. Math. Soc. 84 (1957), 430 – 443. · Zbl 0077.25603
[122] A. A. Albert and N. Jacobson, On reduced exceptional simple Jordan algebras, Ann. of Math. (2) 66 (1957), 400 – 417. · Zbl 0079.04604 · doi:10.2307/1969898
[123] A. A. Albert, A property of ordered rings, Proc. Amer. Math. Soc. 8 (1957), 128 – 129. · Zbl 0081.26401
[124] A. A. Albert and John Thompson, Two element generation of the projective unimodular group, Bull. Amer. Math. Soc. 64 (1958), 92 – 93. · Zbl 0082.02605
[125] A. A. Albert, Addendum to the paper on partially stable algebras, Trans. Amer. Math. Soc. 87 (1958), 57 – 62. · Zbl 0083.02603
[126] A. A. Albert, A construction of exceptional Jordan division algebras, Ann. of Math. (2) 67 (1958), 1 – 28. · Zbl 0079.04701 · doi:10.2307/1969922
[127] A. A. Albert, On the orthogonal equivalence of sets of real symmetric matrices, J. Math. Mech. 7 (1958), 219 – 235. · Zbl 0087.01203
[128] A. A. Albert, A solvable exceptional Jordan algebra, J. Math. Mech. 8 (1959), 331 – 337. · Zbl 0204.04101
[129] A. A. Albert and L. J. Paige, On a homomorphism property of certain Jordan algebras, Trans. Amer. Math. Soc. 93 (1959), 20 – 29. · Zbl 0089.02001
[130] A. A. Albert and John Thompson, Two-element generation of the projective unimodular group, Illinois J. Math. 3 (1959), 421 – 439. · Zbl 0098.02302
[131] A. A. Albert, Finite noncommutative division algebras, Proc. Amer. Math. Soc. 9 (1958), 928 – 932. · Zbl 0092.03501
[132] A. A. Albert, Finite division algebras and finite planes, Proc. Sympos. Appl. Math., Vol. 10, American Mathematical Society, Providence, R.I., 1960, pp. 53 – 70.
[133] A. A. Albert, On the collineation groups associated with twisted fields, Calcutta Math. Soc. Golden Jubilee Commemoration Vol. (1958/59), Part II, Calcutta Math. Soc., Calcutta, 1958/1959, pp. 485 – 497.
[134] A. A. Albert, On the collineation groups of certain non-desarguesian planes, Portugal. Math. 18 (1959), 207 – 224. · Zbl 0099.15203
[135] A. A. Albert, Generalized twisted fields, Pacific J. Math. 11 (1961), 1 – 8. · Zbl 0154.27203
[136] A. A. Albert, Isotopy for generalized twisted fields, An. Acad. Brasil. Ci. 33 (1961), 265 – 275. · Zbl 0154.27301
[137] A. A. Albert, On involutorial associative division algebras, Scripta Math. 26 (1963), 309 – 316 (1963). · Zbl 0147.28702
[138] A. A. Albert, On the nuclei of a simple Jordan algebra, Proc. Nat. Acad. Sci. U.S.A. 50 (1963), 446 – 447. · Zbl 0115.02702
[139] Abraham Adrian Albert, Finite planes for the high school, The Math. Teacher 55 (1962), 165-169.
[140] A. A. Albert, A normal form for Reimann matrices, Canad. J. Math. 17 (1965), 1025 – 1029. · Zbl 0196.30104 · doi:10.4153/CJM-1965-097-0
[141] A. A. Albert, On exceptional Jordan division algebras, Pacific J. Math. 15 (1965), 377 – 404. · Zbl 0135.07202
[142] A. A. Albert, On associative division algebras of prime degree, Proc. Amer. Math. Soc. 16 (1965), 799 – 802. · Zbl 0135.07402
[143] A. A. Albert, The finite planes of Ostrom, Bol. Soc. Mat. Mexicana (2) 11 (1966), 1 – 13. · Zbl 0157.27003
[144] A. A. Albert, New results on associative division algebras, J. Algebra 5 (1967), 110 – 132. · Zbl 0144.02503 · doi:10.1016/0021-8693(67)90030-0
[145] A. A. Albert, On some properties of biabelian fields, An. Acad. Brasil. Ci. 38 (1966), 217 – 221. · Zbl 0154.03903
[146] A. A. Albert, On certain polynomial systems, Scripta Math. 28 (1967), 15 – 19 (1967). · Zbl 0152.02302
[147] A. A. Albert, On associative division algebras, Bull. Amer. Math. Soc. 74 (1968), 438 – 454. · Zbl 0157.08001
[148] A. A. Albert, A note on certain cyclic algebras, J. Algebra 14 (1970), 70 – 72. · Zbl 0186.06901 · doi:10.1016/0021-8693(70)90133-X
[149] A. A. Albert, Tensor products of quaternion algebras, Proc. Amer. Math. Soc. 35 (1972), 65 – 66. · Zbl 0263.16012
[150] S. A. Amitsur, On central division algebras, Israel J. Math. 12 (1972), 408 – 420. · Zbl 0248.16006 · doi:10.1007/BF02764632
[151] Richard Block, New simple Lie algebras of prime characteristic, trans. Amer. Math. Soc. 89 (1958), 421 – 449. · Zbl 0082.25104
[152] Richard Brauer, Über Systeme hyperkomplexer Zahlen, Math. Z. 30 (1929), no. 1, 79 – 107 (German). · JFM 55.0088.02 · doi:10.1007/BF01187754
[153] Richard Brauer, Untersuchungen über die arithmetischen Eigenschaften von Gruppen linearer Substitutionen, Math. Z. 31 (1930), no. 1, 733 – 747 (German). · JFM 56.0865.04 · doi:10.1007/BF01246444
[154] R. Brauer, On normal division algebras of index five, Proc. Nat. Acad. Sci. U.S.A. 24 (1938), 243-246. · Zbl 0019.00206
[155] R. Brauer, H. Hasse and E. Noether, Beweis eines Hauptsatzes in der Theorie der Algebren, J. Reine Angew. Math. 167 (1931), 399-404. · JFM 58.0142.03
[156] F. Cecioni, Sopra un tipo di algebre prive di divisore dello zero, Rend. Circ. Mat. Palermo 47 (1923), 209-254. · JFM 49.0088.02
[157] P. M. Cohn, On homomorphic images of special Jordan algebras, Canadian J. Math. 6 (1954), 253 – 264. · Zbl 0055.02704
[158] L. E. Dickson, New division algebras, Trans. Amer. Math. Soc. 28 (1926), no. 2, 207 – 234. · JFM 52.0133.03
[159] L. E. Dickson, Construction of division algebras, Trans. Amer. Math. Soc. 32 (1930), no. 2, 319 – 334. · JFM 56.0868.03
[160] Marguerite Straus Frank, A new class of simple Lie algebras, Proc. Nat. Acad. Sci. U. S. A. 40 (1954), 713 – 719. · Zbl 0055.26503
[161] Helmut Hasse, Zum Existenzsatz von Grunwald in der Klassenkörpertheorie, J. Reine Angew. Math. 188 (1950), 40 – 64 (German). · Zbl 0039.03102 · doi:10.1515/crll.1950.188.40
[162] G. Hochschild, Semi-simple algebras and generalized derivations, Amer. J. Math. 64 (1942), 677 – 694. · Zbl 0063.02028 · doi:10.2307/2371713
[163] F. D. Jacobson and N. Jacobson, Classification and representation of semi-simple Jordan algebras, Trans. Amer. Math. Soc. 65 (1949), 141 – 169. · Zbl 0034.16902
[164] N. Jacobson, A note on non-associative algebras, Duke Math. J. 3 (1937), no. 3, 544 – 548. · Zbl 0018.05005 · doi:10.1215/S0012-7094-37-00343-0
[165] N. Jacobson, A theorem on the structure of Jordan algebras, Proc. Nat. Acad. Sci. U.S.A. 42 (1956), 140 – 147. · Zbl 0074.02401
[166] Nathan Jacobson, Structure and representations of Jordan algebras, American Mathematical Society Colloquium Publications, Vol. XXXIX, American Mathematical Society, Providence, R.I., 1968. · Zbl 0218.17010
[167] P. Jordan, Über eine Klasse nichtassoziativer hyperkomplexer Algebren, Nachr. Ges. Wiss. Göttingen 1932, 569-575. · JFM 58.0135.02
[168] P. Jordan, J. von Neumann, and E. Wigner, On an algebraic generalization of the quantum mechanical formalism, Ann. of Math. (2) 35 (1934), no. 1, 29 – 64. · JFM 60.0902.02 · doi:10.2307/1968117
[169] G. K. Kalisch, On special Jordan algebras, Trans. Amer. Math. Soc. 61 (1947), 482 – 494. · Zbl 0032.25003
[170] Erwin Kleinfeld, Simple alternative rings, Ann. of Math. (2) 58 (1953), 544 – 547. · Zbl 0051.02503 · doi:10.2307/1969753
[171] Erwin Kleinfeld, Alternative nil rings, Ann. of Math. (2) 66 (1957), 395 – 399. · Zbl 0079.26101 · doi:10.2307/1969897
[172] A. I. Kostrikin and I. R. Šafarevič, Graded Lie algebras of finite characteristic, Izv. Akad. Nauk SSSR Ser. Mat. 33 (1969), 251 – 322 (Russian).
[173] Kevin McCrimmon, Finite power-associative division rings, Proc. Amer. Math. Soc. 17 (1966), 1173 – 1177. · Zbl 0145.25701
[174] Kevin McCrimmon, A note on finite division rings, Proc. Amer. Math. Soc. 23 (1969), 598 – 600. · Zbl 0218.17001
[175] M. L. Racine, A note on quadratic Jordan algebras of degree 3, Trans. Amer. Math. Soc. 164 (1972), 93 – 103. · Zbl 0236.17007
[176] C. Rosati, Sulle matrici di Riemann, Rend. Circ. Mat. Palermo 53 (1929), 79-134. · JFM 55.0810.02
[177] K. Soda, Einige Sätze über Matrizen, Japan J. Math. 13 (1936), 361-365. · JFM 63.0842.03
[178] C. L. Siegel, Lectures on Riemann matrices, Notes by S. Raghavan and S. S. Rangachari. Tata Institute of Fundamental Research Lectures on Mathematics, No. 28, Tata Institute of Fundamental Research, Bombay, 1963. · Zbl 0249.14014
[179] T. A. Springer, The classification of reduced exceptional simple Jordan algebras, Nederl. Akad. Wetensch. Proc. Ser.A 63 = Indag. Math. 22 (1960), 414 – 422. · Zbl 0098.02901
[180] O. Teichmüller, Multiplikation zyklischer Normalringen, Deutsch. Math. 1936, 197-238. · Zbl 0014.24904
[181] O. Teichmüller, p-Algebren, Deutsch. Math. 1936, 362-388. · JFM 62.0101.03
[182] Shianghaw Wang, A counter-example to Grunwald’s theorem, Ann. of Math. (2) 49 (1948), 1008 – 1009. · Zbl 0032.10802 · doi:10.2307/1969410
[183] Shianghaw Wang, On Grunwald’s theorem, Ann. of Math. (2) 51 (1950), 471 – 484. · Zbl 0036.15802 · doi:10.2307/1969335
[184] J. H. M. Wedderburn, A type of primitive algebra, Trans. Amer. Math. Soc. 15 (1914), no. 2, 162 – 166. · JFM 45.0189.04
[185] J. H. M. Wedderburn, On division algebras, Trans. Amer. Math. Soc. 22 (1921), no. 2, 129 – 135. · JFM 48.0126.01
[186] Hermann Weyl, On generalized Riemann matrices, Ann. of Math. (2) 35 (1934), no. 4, 714 – 729. · Zbl 0010.10003 · doi:10.2307/1968487
[187] Hermann Weyl, Generalized Riemann matrices and factor sets, Ann. of Math. (2) 37 (1936), no. 3, 709 – 745. · Zbl 0015.29201 · doi:10.2307/1968485
[188] D. Zelinsky, A. A. Albert, Amer. Math. Monthly 80 (1973), 661 – 665. · Zbl 0264.01019 · doi:10.2307/2319167
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