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 …

I include a complete proof of this result in this survey article. My emphasis lies on the
conscruction of maximal Cohen-Macaulay modules via matrix factorizations (section 2), from …

This work is concerned with both strong generation and (co) ghost index in the module
category of a commutative noetherian ring. A sufficiency criterion is established for such …

This book is a lightly edited version of the unpublished manuscript Maximal Cohen–
Macaulay modules and Tate cohomology over Gorenstein rings by Ragnar-Olaf Buchweitz …

The cohomology annihilator of a noetherian ring that is finitely generated as a module over
its center is introduced. Results are established linking the existence of nontrivial …

Throughout this paper we assume that K is a field. Given a K-algebra A we denote by mod
(A) the category of finitely generated right A-modules and by fin (A) the full subcategory of …

Let ℤ denote the integers and R= ∐ i ∈ Z R_i a ℤ-graded commutative ring with R 0= ka
field, R i=(0) when i< 0, and where R is generated as ak-algebra by a finite number of …

Let be a commutative noetherian local ring of Krull dimension. We prove that the
cohomology annihilator of contains a power of if and only if, for some the th syzygies in are …

Let R be a commutative Noetherian ring. We prove that if R is either an equidimensional
finitely generated algebra over a perfect field, or an equidimensional equicharacteristic …

The purpose of this survey is to introduce some of the ideas and results in the theory of finite
dimensional algebras to researchers in singularity theory and the theory of vector bundles …