Abstract The notions of Cohen-Macaulay and Gorenstein rings, as well as Cohen-Macaulay
modules, are well established in commutative noetherian ring theory. In [6] we introduced …

An artin algebra A is said to be CM-finite if there are only finitely many, up to isomorphisms,
indecomposable finitely generated Gorenstein-projective A-modules. We prove that for a …

An Artin algebra A is said to be CM-finite if there are only finitely many isomorphism classes
of indecomposable finitely generated Gorenstein-projective A-modules. Inspired by …

A graded Artin algebra is a graded ring which, neglecting the grading, is an Artin algebra.
Although this definition has the merit of brevity, it does not expose some of the basic …

Publisher Summary This chapter discusses large modules over artin algebras. An artin ring
Λ is said to be an artin algebra if its center C is an artin ring and Λ is a finitely generated …

This book is intended to provide a reasonably self-contained account of a major portion of
the general theory of rings and modules suitable as a text for introductory and more …

Auslander conjectured that every Artin algebra satisfies a certain condition on vanishing of
cohomology of finitely generated modules. The failure of this conjecture—by a 2003 …

We study Artin algebras Λ and commutative Noetherian complete local rings R in connection
with the following decomposition property of Gorenstein-projective modules: We show that …

An Artin algebra is by definition virtually Gorenstein if the class of modules which are right
orthogonal (with respect to $\operatorname {Ext}^*(-,-) $) to all Gorenstein projective …

We use torsion pairs in stable categories and cotorsion pairs in modules categories to study,
in general infinitely generated, Cohen–Macaulay modules and (a generalization of) …