Abstract Let $ A $ and $ B $ be rings, $ U $ a $(B, A) $-bimodule, and $ T=\left (\begin
{smallmatrix} A & 0\\U & B\\\end {smallmatrix}\right) $ the triangular matrix ring. In this paper …

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

In this paper, we extend the well-known Hilbert's syzygy theorem to the Gorenstein
homological dimensions of rings. Also, we study the Gorenstein homological dimensions of …

The principle “Every result in classical homological algebra should have a counterpart in
Gorenstein homological algebra” was given by Henrik Holm. There is a remarkable body of …

In basic homological algebra, projective, injective and flat modules play an important and
fundamental role. In this paper, we discuss some properties of Gorenstein projective …

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 …

Let 𝒜 be an abelian category. In this paper, we investigate the global (𝒳, 𝒴)-Gorenstein
projective dimension gl. GPD (𝒳, 𝒴)(𝒜), associated to a GP-admissible pair (𝒳, 𝒴). We give …

In this paper, we examine the class of modules of finite Gorenstein projective dimension and
study approximations of modules in that class by modules which are either Gorenstein …

We introduce the notion of relative singularity category with respect to a self‐orthogonal
subcategory ω of an abelian category. We introduce the Frobenius category of ω‐Cohen …

The theory of Gorenstein injective and projective modules start, ed in [4] as an st, udy of
homology for Gorenstein rings, ie, rings which are noetherian on both sides and with finite …