In a previous paper [5] relationships between homological dimensions of rings with
countably generated ideals have been considered. It is the purpose of this note to extend …

Let R be an arbitrary, not necessarily commutative ring with an identity element. A left A-
module Α Φ 0 is said to have homological dimension n, denoted l. dh^ A), if A has a …

Relationships between homological dimensions of Noetherian rings and duality conditions
on finitely generated modules have been studied in [1],[4], In this paper we consider …

In this paper I shall demonstrate certain algebraic properties of ideals of finite homological
dimension in local rings. In the first section, I show that no non-zero ideal of finite …

1. Introduction.-It is our purpose in this note to present some new results in the theory of
commutative Noetherian rings (with special emphasis on local rings) which we have …

Introduction. Throughout this paper it is assumed that all rings are commutative, noetherian
rings with unit element and all modules are unitary. The major purpose of this paper is to …

Introduction. This paper is devoted primarily to the study of commuta-tive noetherian local
rings. The main task is to compare purely algebraic properties with properties of a …

Let $\{e (i)| i\in\mathcal {I}\} $ be an infinite set of commuting idempotents in a ring R with 1
such that\[\prod\limits _ {\alpha= 0}^ n {e ({i_\alpha})\prod\limits _ {\beta= n+ 1}^ m {(1-e …

We shall consider a semi-primary ring ۸ with radical N (ie N is nilpotent and ۸/N is semi-
simple (with minimum condition)). All modules considered are left ۸-modules. We refer to [1] …

Let R be a ring with identity element 1, and let S be a subring of R containing 1. We consider
R-modules on which 1 acts as the identity map, and we shall simultaneously regard such R …