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On the Dimension of Modules and Algebras, V. Dimension of Residue Rings

Published online by Cambridge University Press:  22 January 2016

Samuel Eilenberg  and
Tadasi Nakayama
Samuel Eilenberg
Affiliation:
Columbia University
Tadasi Nakayama
Affiliation:
Nagoya University and The Institute for Advanced Study
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We shall consider a semi-primary ring ۸ with radical N (i.e. N is nilpotent and ۸/N is semi-simple (with minimum condition)). All modules considered are left ۸-modules. We refer to [1] for all notions relevant to homological algebra.

The objective of this paper is to establish the following two theorems:

Theorem I. Let a be a two-sided ideal in A such that

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 11 , February 1957 , pp. 9 - 12
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1957

References

[1] Cartan, H. and Eilenberg, S., Homological Algebra, Princeton Univ. Press, 1956.Google Scholar
[2] Eilenberg, S., Homological dimension and syzygies, Ann. Math., 64 (1956), 328–336.CrossRefGoogle Scholar
[3] Eilenberg, S., Nagao, H. and Nakayama, T., On the dimension of modules and algebras, IV, Nagoya Math. J., 10 (1956), 87–95.CrossRefGoogle Scholar