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 …

Auslander conjectured that every Artin algebra satisfies a certain condition on vanishing of
cohomology of finitely generated modules. The failure of this conjecture—by a 2003 …

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 …

Conditions on the Koszul complex of a noetherian local ring R guarantee that Tor i R (M, N)
is nonzero for infinitely many i, when M and N are finitely generated R-modules of infinite …

A semidualizing module is a generalization of Grothendieck's dualizing module. For a local
Cohen-Macaulay ring $ R $, the ring itself and its canonical module are always realized as …

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 …

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 …

The notion of local rings with quasi-decomposable maximal ideal was formally introduced by
Nasseh and Takahashi. In separate works, the authors of the present paper showed that …

Let $(R,\mathfrak {m}, k) $ be a Noetherian local ring and let $ M $ be a finitely generated $
R $-module. The main focus of this paper is to give positive answers for some long-standing …

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 …