This article is an extended and completed version of the second part of the joint survey
lecture with Yu. Drozd on Cohen-Macaulay modules over Cohen-Macaulay algebras …

The local cohomology theory introduced by Grothendieck (1) is a useful tool for attacking
problems in commutative algebra and algebraic geometry. Let A denote a local ring with its …

Given surjective homomorphisms R→ T← S of local rings, and ideals in R and S that are
isomorphic to some T-module V, the connected sum R⋕ TS is defined to be the ring …

We consider the homotopy category of complexes of projective modules over a Noetherian
ring. Truncation at degree zero induces a fully faithful triangle functor from the totally acyclic …

We apply constructions from equivariant topology to Benson-Carlson resolutions and hence
prove in (2.1) that the group cohomology ring of a finite group enjoys remarkable duality …

This paper analyzes the graded maximal Cohen-Macaulay modules over rings of the form
R= k [x 1,..., xr]/Q, when Q is a quadratic form defining a regular projective hypersurface, and …

Its construction and some of its properties are described in [7, w 2]. The Krull dimension of a
non-zero A-module M [7,(1.7) 3 will be denoted in this article by dimAM. For such an M, the …

Artin-Nagata properties and Cohen-Macaulay associated graded rings Page 1
COMPOSITIO MATHEMATICA MARK JOHNSON BERND ULRICH Artin-Nagata properties …

This is a survey paper based on my talks at the 41st Symposium on Ring Theory and
Representation Theory, held in Shizuoka University, Japan in September 2008, and will …

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 …