There are different approaches to characterizing the structures of commutative rings: the
category of modules over commutative rings, homology theories, theories of the star …

Consider a non-trivial fiber product $ R= S\times _kT $ of local rings $ S $, $ T $ with
common residue field $ k $. Given two finitely generated $ R $-modules $ M $ and $ N $, we …

We describe new classes of noetherian local rings R whose finitely generated modules M
have the property that Tor i R (M, M)= 0 for i≫ 0 implies that M has finite projective …

Given two positive integers e and s we consider Gorenstein Artinian local rings R whose
maximal ideal m satisfies ms≠ 0= m s+ 1 and rank R/m (m/m 2)= e. We say that R is a …

The notion of naive lifting of DG modules was introduced by the authors in [16, 17] for the
purpose of studying problems in homological commutative algebra that involve self …

Let n be a positive integer, and let A be a strongly commutative differential graded (DG)
algebra over a commutative ring R. Assume that B= A [X 1,…, X n] is a polynomial extension …

We further develop the theory of generalized Ulrich modules introduced in 2014 by Goto et
al. Our main goal is to address the problem as to when the operations of taking the Hom …

We introduce the finitistic extension degree of a ring and investigate rings for which it is
finite. The Auslander–Reiten Conjecture is proved for rings of finite finitistic extension …

A commutative Noetherian ring R is said to be Tor-persistent if, for any finitely generated R-
module M, the vanishing of Tor i R (M, M) for i≫ 0 implies M has finite projective dimension …

The long-standing Auslander and Reiten Conjecture states that a finitely generated module
over a finite-dimensional algebra is projective if certain Ext-groups vanish. Several authors …