论文信息 - On the Dimension of Modules and Algebras, V. Dimension of Residue Rings

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

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

S. Eilenberg | T. Nakayama

[1] S. Eilenberg. Homological Dimension and Syzygies , 1956 .

[2] S. Eilenberg,et al. On the Dimension of Modules and Algebras, IV: Dimension of Residue Rings of Hereditary Rings , 1956, Nagoya Mathematical Journal.

[3] S. Eilenberg,et al. On the Dimension of Modules and Algebras, I , 1955, Nagoya Mathematical Journal.

[4] S. Eilenberg,et al. On the Dimension of Modules and Algebras, II: (Frobenius Algebras and Quasi-Frobenius Rings) , 1955, Nagoya mathematical journal.