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

Abstract

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