A question of Avramov and Foxby concerning injective dimension of complexes is settled in
the affirmative for the class of noetherian rings. A key step in the proof is to recast the …

This note presents the definitions of homological dimensions of bounded complexes of
modules as proposed by the author in [3]. Somewhat different definitions have been …

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. If R is a ring and M a left R-module, then homological algebra attaches three
dimensions to M, projective, weak, and injective (l). By taking the supremum of one of these …

INTRODUCTION. The main results of this paper show that homological dimensions over a
fully bounded noetherian (FBN) ring R may be computed using just simple R-modules, as …

This paper explores various notions of projective, injective, and flat dimensions, arising from
recent constructions of resolutions of unbounded complexes, proposed by N. Spaltenstein …

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 …

We prove that (a) if R is a commutative coherent ring, the weak global dimension of R equals
the supremum of the flat (or (FP–) injective) dimensions of the simple R-modules;(b) if R is …

Cohen-Macaulay dimension for modules over a commutative ring has been defined by AA
Gerko. That is a homological invariant sharing many properties with projective dimension …

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 …