If the algebra is a group algebra KG (or a block B), then properties of the group are related to
the graph structure of the Auslander-Reiten quiver. For example, the graph f (KG)(or T (B)) is …

It was proved by Avramov and Buchweitz that if A is a commutative local complete
intersection ring with finitely generated modules M and N, then the Ext groups between M …

Presently two classes of artinian rings are known, over which there exist Auslander-Reiten
sequences: artin algebras and rings of finite representation type. To be more precise …

Let R be a commutative Noetherian ring, a an element of R, and M a nonzero finitely
generated R-module. We study the nonvanishing of Ext R 1 (R∕ R a, M) and we give some …

A recent result of Araya asserts that if the Auslander–Reiten conjecture holds in
codimension one for a commutative Gorenstein ring R, then it holds for R. This note extends …

The paper contains Parts 1, 2, 3, and 4 of a review of the authors on endomorphism rings of
Abelian groups. Most of the results are given with proofs. Part 1 contains some general …

Let R be a left noetherian ring, S a right noetherian ring and UR a generalized tilting module
with S= End (UR). The injective dimensions of UR and US are identical provided both of …

In this paper we review and study $ R $-modules $ M $ for which $ S= End_R (M) $ is
commutative. For this, we define the concept of center of modules which is a natural …

Finitary and Artinian-finitary groups over commutative rings Page 1 J. Group Theory 7 (2004),
243–253 Journal of Group Theory ( de Gruyter 2004 Finitary and Artinian-finitary groups over …

Generic modules were introduced by Crawley-Boevey in order to provide a better
understanding of finite-dimensional algebras of tame representation type. In fact he has …