Motivated by recent work of Knorrer [17], Buchweitz, Greuel and Schreyer [9] who proved
that a hypersurface singularity R over C is of finite Cohen-Macaulay representation type if …

Throughout this note R is an equidimensional commutative Gorenstein ring and A is an R-
algebra which is a finitely generated (maximal) Cohen-Macaulay R-module. We denote by …

Let M be a finitely generated module over a commutative noetherian ring A (with 1). Then M
is called qtcusi-perfect if G-dim M= gradeM. Perfect modules (ie projective dimension …

The purpose of these notes is to explain in detail some topics on the intersection of
commutative algebra, representation theory and singularity theory. They are based on …

This paper contains two theorems concerning the theory of maximal Cohen–Macaulay
modules. The first theorem proves that certain Ext groups between maximal Cohen …

In the last few years the maximal Cohen-Macaulay modules over local rings of singularities
have been studied by methods of representation theory, commutative algebra, and algebraic …

0.1. H. Kn/Srrer [Kn6] showed the following property of the local ring R of an isolated simple
hypersurface singularity: There are only finitely many isomorphism classes of …

We give several characterizations for the linearity property for a maximal Cohen-Macaulay
module over a local or graded ring, as well as proofs of existence in some new cases. In …

Let A be a (commutative, Noetherian) local ring (with identity) and let a1,…, an be a system
of parameters (sop) for A. A (not necessarily finitely generated) A-module M is said to be a …

The purpose of this paper is to prove the existence of linear maximal Cohen-Macaulay
modules over strict complete intersections. Given a maximal Cohen-Macaulay module (an …