This is the second revised edition of an introduction to contemporary relative homological
algebra. It supplies important material essential to understand topics in algebra, algebraic …

Since the injective envelope and projective cover were defined by Eckmann and Bas in the
1960s, they have had great influence on the development of homological algebra, ring …

This book is intended as a reference for mathematicians working with homological
dimensions in commutative algebra and as an introduction to Gorenstein dimensions for …

Gorenstein homological dimensions are refinements of the classical homological
dimensions, and finiteness singles out modules with amenable properties reflecting those of …

Notation. The ring A will always be commutative and noetherian, while G always denote a
finitely generated (fg) non-zero A-module. The endomorphism ring Hom^(G, G) of G will be …

It is not known whether modules over an arbitrary ring have flat covers, however for certain
modules over commutative noetherian rings they can be shown to exist. These covers, in …

In this paper the concept of cocyclic modules is introduced, and it is used to define
coassociated primes and the cosupport of mod-ules. Also it is shown that cocyclic modules …

Throughout this paper, R will denote a commutative noetherian ring. If M is an R-module, we
can construct an injective resolvent of M using injective precovers (see Enochs [5]). If we use …

In 1966, Auslander introduced the notion of the $ G $-dimension of a finitely generated
module over a Cohen-Macaulay noetherian ring and found the basic properties of these …

Ascent Properties of Auslander Categories Page 1 Canad. J. Math. Vol. 61 (1), 2009 pp. 76–108
Ascent Properties of Auslander Categories Lars Winther Christensen and Henrik Holm Abstract …