Let be a morphism of Artin local rings with the same embedding dimension. We prove that
any-flat-module is-flat. This freeness criterion was conjectured by de Smit in 1997 and …

This paper studies vanishing of Ext modules over Cohen–Macaulay local rings. The main
result of this paper implies that the Auslander–Reiten conjecture holds for maximal Cohen …

We give counterexamples to the following conjecture of Auslander: given a finitely
generated module M over an Artin algebra Λ, there exists a positive integer nM such that for …

Following Roos, we say that a local ring $ R $ is good if all finitely generated $ R $-modules
have rational Poincar\'e series over $ R $, sharing a common denominator. Rings with the …

Following the well‐established terminology in commutative algebra, any (not necessarily
commutative) finite‐dimensional local algebra AA with radical JJ will be said to be short …

This paper studies the vanishing of $ Ext $ modules over group rings. Let $ R $ be a
commutative noetherian ring and $ ga $ a group. We provide a criterion under which the …

If $ R $ is a ring with 1, we call a unital left $ R $-module $ M $ co-Hopfian (Hopfian) in the
category of left $ R $-modules if any monic (epic) endomorphism of $ M $ is an …

Let R be a commutative Noetherian ring. We consider the question of when n-syzygy
modules over R are n-torsionfree in the sense of Auslander and Bridger. Our tools include …

In this paper, we investigate the finiteness of Ext-indices for certain ring extensions. In this
direction, we introduce some conjectures and discuss the relationships among them. We …

It is well-known that the generalized Auslander-Reiten condition (GARC) and the symmetric
Auslander condition (SAC) are equivalent, and (GARC) implies that the Auslander-Reiten …