There are different approaches to characterizing the structures of commutative rings: the
category of modules over commutative rings, homology theories, theories of the star …

This book is a comprehensive treatment of the representation theory of maximal Cohen-
Macaulay (MCM) modules over local rings. This topic is at the intersection of commutative …

We study finitely generated modules has finite projective dimension. Comparison
morphisms and link these functors. We give a self-contained treatment of modules of finite G …

Quillen's geometric approach to the cohomology of finite groups [30] has revolutionized
modular representation theory. The ideology and techniques involved have been …

Remarks on a depth formula, a grade inequality and a conjecture of Auslander Page 1
COMMUNICATIONS IN ALGEBRA, 26(1 l), 3793-3806 (1998) Remarks on a depth formula, a …

Weighted projective lines, introduced by Geigle and Lenzing in 1987, are important objects
in representation theory. They have tilting bundles, whose endomorphism algebras are the …

Consider a non-trivial fiber product $ R= S\times _kT $ of local rings $ S $, $ T $ with
common residue field $ k $. Given two finitely generated $ R $-modules $ M $ and $ N $, we …

In this paper, we investigate the maximal Cohen–Macaulay property of tensor products of
modules, and then give criteria for projectivity of modules in terms of vanishing of Ext …

In studying Nakayama's 1958 conjecture on rings of infinite dominant dimension, Auslander
and Reiten proposed the following generalization: Let Λ be an Artin algebra and M a Λ …

We discuss vanishing of cohomology of finite modules over Cohen-Macaulay local rings
$(R,\mathfrak m) $. Special attention is given to the case when the modules are annihilated …