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 …

We say that a Cohen–Macaulay local ring has finite CM+-representation type if there exist
only finitely many isomorphism classes of indecomposable maximal Cohen–Macaulay …

This article explains basic constructions and results on group algebras and their
cohomology, starting from the point of view of commutative algebra. It provides the …

Let R be a reduced, one-dimensional Noetherian local ring whose integral closure R is
finitely generated over R. Since R is a direct product of finitely many principal ideal domains …

In this article, we study Cohen–Macaulay modules over non-reduced curve singularities. We
prove that the rings k [x, y, z]/(xy, yq− z 2) have tame Cohen–Macaulay representation type …

A commutative Noetherian local ring $(R,\mathfrak m, k) $ is called Dedekind-like provided $
R $ is one-dimensional and reduced, the integral closure $\overline {R} $ is generated by at …

In this note, it is shown that the validity of the Auslander–Reiten conjecture for a given d-
dimensional Cohen–Macaulay local ring R depends on its validity for all direct summands of …

In this article we show a partial answer to a question of Huneke and Leuschke (Proc. Am.
Math. Soc. 131 (10): 3003–3007, 2003): Let R be a standard graded Cohen–Macaulay ring …

Abstract The Brauer-Thrall Conjectures, now theorems, were originally stated for finitely
generated modules over a finite-dimensional k-algebra. They say, roughly speaking, that …

In this thesis we solve several classification problems from Lie theory and commutative
algebra. In the main part of this thesis, we study Harish-Chandra modules of some classical …