For a left module M over a ring R, pd (M) and id (M) denote the projective and injective
dimension of M, respectively. A (left and right) noether ring R is called n-Gorenstein for an n> …

For a ring R, we prove that all left R-modules have weak injective covers and weak injective
preenvelopes. Then we characterize the right weak injective dimension of modules in terms …

Let R be a commutative unitary ring with X an analytic indeterminate. Unlike the situation for
polynomial rings, the weak global dimension of the power series ring R [[X]] need not be …

The notion of dominant dimension, äs introduced for finite-dimensional algebras over fields
by Nakayama [15] and Tachikawa [17], generalizes immediately to arbitrary rings: right …

The left finitistic dimension of a left artinian ring R, denoted by lfPD (R), is defined to be the
supremum of the projective dimension of those finitely generated left R-modules which have …

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

A left R-module RM is said to have an injective resolution with a redundant (strongly
redundant) image from an integer n> 1 in case the nth cosyzygy 52, has a decomposition fl …

Essential Domains and Two Conjectures in Dimension Theory Page 1 PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY Volume 132, Number 9, Pages 2529-2535 S …

Homological dimensions of some pirings Page 1 COMMJNICATIONS IN ALGEBRA, 8(7),
685-696 (1980) HONOLOGICAL DINENSIONS OF SOME PI RINGS. S. Jondrup. Department …

We define three new homological dimensions: Cohen-Macaulay injective, projective, and
flat dimension, and show that they inhabit a theory similar to that of classical injective …