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Homological dimension in local rings. (English) Zbl 0078.02802

Lattices; Rings; Fields
Full Text: DOI
[1] Maurice Auslander, On the dimension of modules and algebras. III. Global dimension, Nagoya Math. J. 9 (1955), 67 – 77. · Zbl 0067.27103
[2] Maurice Auslander and David A. Buchsbaum, Homological dimension in Noetherian rings, Proc. Nat. Acad. Sci. U.S.A. 42 (1956), 36 – 38. · Zbl 0070.03503
[3] Henri Cartan and Samuel Eilenberg, Homological algebra, Princeton University Press, Princeton, N. J., 1956. · Zbl 0075.24305
[4] I. S. Cohen, On the structure and ideal theory of complete local rings, Trans. Amer. Math. Soc. 59 (1946), 54 – 106. · Zbl 0060.07001
[5] Wolfgang Gröbner, Moderne algebraische Geometrie. Die idealtheoretischen Grundlagen, Springer-Verlag, Wien und Innsbruck, 1949 (German). · Zbl 0033.12706
[6] W. Krull, Dimensiontheorie in Stellenringen, J. Crelle vol. 179 (1938). · JFM 64.0078.02
[7] D. G. Northcott, Ideal theory, Cambridge Tracts in Mathematics and Mathematical Physics, No. 42, Cambridge, at the University Press, 1953. · Zbl 0052.26801
[8] P. Samuel, Commutative algebra (Notes by D. Hertzig), Cornell University, 1953.
[9] J.-P. Serre, Faisceaux algébriques cohérents, Ann. of Math. vol. 61 (1955). · Zbl 0067.16201
[10] -, Sur la dimension des anneaux et des modules noethériens, Proceedings of the International Symposium on Algebraic Number Theory, Tokyo and Nikko, 1955, Science Council of Japan, Tokyo, 1956.
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