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On the deformation of commutative algebras. (English) Zbl 0199.36102

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[1] N. Bourbaki, Éléments de mathématique. Première partie. Fascicule VI. Livre II: Algèbre. Chapitre 2: Algèbre linéaire, Troisième édition, entièrement refondue, Actualités Sci. Indust., No. 1236. Hermann, Paris, 1962 (French).
[2] -, Algèbre commutative, Actualités Sci. Indust., No. 1290, Hermann, Paris, 1961.
[3] -, Algèbre commutative, Actualités Sci. Indust., No. 1293, Hermann, Paris, 1961.
[4] Henri Cartan and Samuel Eilenberg, Homological algebra, Princeton University Press, Princeton, N. J., 1956. · Zbl 0075.24305
[5] P. Cartier, Dérivations dans les corps, Séminaire H. Cartan et C. Chevalley, 8e année, 1955-1956, exposé 13.
[6] Murray Gerstenhaber, The cohomology structure of an associative ring, Ann. of Math. (2) 78 (1963), 267 – 288. · Zbl 0131.27302
[7] Murray Gerstenhaber, On the construction of division rings by the deformation of fields, Proc. Nat. Acad. Sci. U.S.A. 55 (1966), 690 – 692. · Zbl 0136.31401
[8] Murray Gerstenhaber, On the deformation of rings and algebras, Ann. of Math. (2) 79 (1964), 59 – 103. · Zbl 0123.03101
[9] A. Grothendieck, Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes de schémas. I, Inst. Hautes Études Sci. Publ. Math. No. 20 (1964). · Zbl 0136.15901
[10] Alexander Grothendieck, Sur quelques points d’algèbre homologique, Tôhoku Math. J. (2) 9 (1957), 119 – 221 (French). · Zbl 0118.26104
[11] D. K. Harrison, Commutative algebras and cohomology, Trans. Amer. Math. Soc. 104 (1962), 191 – 204. · Zbl 0106.25703
[12] Robin Hartshorne, Complete intersections and connectedness, Amer. J. Math. 84 (1962), 497 – 508. · Zbl 0108.16602
[13] G. Hochschild, On the cohomology theory for associative algebras, Ann. of Math. (2) 47 (1946), 568 – 579. · Zbl 0063.02030
[14] G. Hochschild, Bertram Kostant, and Alex Rosenberg, Differential forms on regular affine algebras, Trans. Amer. Math. Soc. 102 (1962), 383 – 408. · Zbl 0102.27701
[15] Nathan Jacobson, Lectures in abstract algebra. Vol III: Theory of fields and Galois theory, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London-New York, 1964. · Zbl 0124.27002
[16] S. MacLane, Homology, Springer-Verlag, Berlin, 1963. · Zbl 0133.26502
[17] A. Nijenhuis, Graded Lie algebras and their applications, Universiteit van Amsterdam, Mimeographed Notes, 1964.
[18] Alex Rosenberg and Daniel Zelinsky, Cohomology of infinite algebras, Trans. Amer. Math. Soc. 82 (1956), 85 – 98. · Zbl 0070.26902
[19] P. Samuel, Méthodes d’algèbre abstraite en géométrie algébrique, Ergebnisse der Mathematik und ihrer Grenzgebiete (N.F.), Heft 4, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1955 (French). · Zbl 0146.16901
[20] Jean-Pierre Serre, Algèbre locale. Multiplicités, Cours au Collège de France, 1957 – 1958, rédigé par Pierre Gabriel. Seconde édition, 1965. Lecture Notes in Mathematics, vol. 11, Springer-Verlag, Berlin-New York, 1965 (French). · Zbl 0142.28603
[21] Satoshi Suzuki, On torsion of the module of differentials of a locality which is a complete intersection, J. Math. Kyoto Univ. 4 (1964/1965), 471 – 475. · Zbl 0127.26102
[22] Oscar Zariski and Pierre Samuel, Commutative algebra. Vol. II, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N. J.-Toronto-London-New York, 1960. · Zbl 0322.13001
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