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Über Halbringe und Halbkörper. I, II. (German) Zbl 0125.01002


MSC:

16Y60 Semirings
12K10 Semifields
Full Text: DOI

References:

[1] R. Baer, Inverses and zero-divisors,Bull. Amer. Math. Soc. 48 (1942), S. 630–638. · Zbl 0060.07103 · doi:10.1090/S0002-9904-1942-07750-0
[2] G. Birkhoff,Lattice theory (2. Aufl., New York, 1948). · Zbl 0033.10103
[3] S. Bourne, The Jacobson radical of a semiring,Proc. Nat. Acad. Sci. of USA,37 (1951), S. 163–170. · Zbl 0042.03201 · doi:10.1073/pnas.37.3.163
[4] S. Bourne, On multiplicative idempotents of a potent semiring,Proc. Nat. Acad. Sci. of USA,42 (1956), S. 632–638. · Zbl 0071.25602 · doi:10.1073/pnas.42.9.632
[5] S. Bourne, H. Zassenhaus, On a Wedderburn-Artin structure theory of a potent semiring,Proc. Nat. Acad. Sci. of USA,43 (1957), S. 613–615. · Zbl 0078.02101 · doi:10.1073/pnas.43.7.613
[6] S. Bourne, H. Zassenhaus, On the semiradical of a semiring,Proc. Nat. Acad. Sci. of USA,44 (1958), S. 907–914. · Zbl 0084.03403 · doi:10.1073/pnas.44.9.907
[7] S. Bourne, On compakt semirings,Proc. Jap. Acad.,35 (1959), S. 332–334. · Zbl 0092.03005 · doi:10.3792/pja/1195524283
[8] S. Bourne, On the radical of a positiv semiring,Proc. Nat. Acad. Sci. of USA,45 (1959), S. 519. · Zbl 0092.03001 · doi:10.1073/pnas.45.10.1519
[9] K. Iseki, Y. Miyanaga, Notes on topological spaces. III, IV,Proc. Jap. Acad.,32 (1956), S. 325–328; 392–395. · Zbl 0070.02803 · doi:10.3792/pja/1195525375
[10] K. Iseki, Notes on topological spaces. V,Proc. Jap. Acad.,32 (1956), S. 426–429. · Zbl 0072.40302 · doi:10.3792/pja/1195525309
[11] K. Iseki, Idealtheory of semirings,Proc. Jap. Acad.,32 (1956), S. 554–559. · Zbl 0073.01902 · doi:10.3792/pja/1195525272
[12] K. Iseki, Y. Miyanaga, On a radical in a semiring,Proc. Jap. Acad.,32, (1956), S. 562–563. · Zbl 0073.01903 · doi:10.3792/pja/1195525274
[13] K. Iseki, Ideals in semirings,Proc. Jap. Acad.,34 (1958), S. 29–31. · Zbl 0092.03003 · doi:10.3792/pja/1195524845
[14] K. Iseki, Quasiideals in semirings without zero,Proc. Jap. Acad.,34 (1958), S. 79–81. · Zbl 0080.25401 · doi:10.3792/pja/1195524783
[15] K. Iseki, On ideals in semiring,Proc. Jap. Acad.,34 (1958), S. 507–509. · Zbl 0085.02101 · doi:10.3792/pja/1195524563
[16] N. Kimura, The structure of idempotent semigroups (I),Pacific J.,8 (1958), S. 257–275. · Zbl 0084.02702 · doi:10.2140/pjm.1958.8.257
[17] L. Rédel,Algebra. l, deutsche Ausg. (Leipzig, 1959).
[18] W. Slowikowski W. Zawadowski, A generalization of maximal ideals method of Stone and Gelfand,Fund. ath.,42 (1955), S. 216–231.
[19] O. Steinfeld, Über die Struktursätze der Semiringe,Acta Math. Acad. Sci. Hung.,10 (1959), S. 149–155. · Zbl 0087.02801 · doi:10.1007/BF02063296
[20] H. S. Vandiver, Note on a simple type of algebra in which the cancellation law of addition does not hold,Bull. Amer. Math. Soc.,40 (1934), S. 914–920. · Zbl 0010.38804 · doi:10.1090/S0002-9904-1934-06003-8
[21] H. S. Vandiver, On some simple types of semirings,Am. Math. Monthly. 46 (1939), S. 22–26. · Zbl 0020.19904 · doi:10.2307/2302918
[22] H. S. Vandiver, On the imbedding of one semigroup in another with application to semirings,Am. J.,62 (1940), S. 72–78. · JFM 66.0097.03
[23] H. S. Vandiver, A development of associative algebra and an algebraic theory of numbers. I, II,Math. Mag.,25 (1952);27 (1954). · Zbl 0049.30601
[24] H. S. Vandiver-M. W. Weaver, A development of associative algebra and an algebraic theory of numbers. III, IV,Math. Mag.,29 (1955);30 (1956).
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