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 …

Assume that ϕ (R, m, k)→(S, n, l) is a local homomorphism between commutative noetherian
local rings R and S. We say that an S-module M is almost finite over R if it is finitely …

The question of whether an injective module E over a noncommutative noetherian ring R
remains injective after localization with respect to a denominator set X⊆ R is addressed.(For …

Let R be a commutative Noetherian local ring and M, N be finitely generated R-modules. We
prove a number of results of the form: if Hom R (M, N) has some nice properties and Ext R …

Let $ R $ be a commutative noetherian local ring. Denote by $\mod R $ the category of
finitely generated $ R $-modules, and by ${\mathcal G}(R) $ the full subcategory of $\mod R …

Considering modules of finite complete intersection dimension over commutative
Noetherian local rings, we prove (co) homology vanishing results in which we assume the …

Throughout this paper we assume that all rings are commutative, noetherian rings with unit
and that all modules are finitely generated and unitary. The main object of study is what it …

Let R be a commutative Noetherian ring. Let P (R)(respectively, I (R)) be the category of all
finite R-modules of finite projective (respectively, injective) dimension. Sharp [9] constructed …

We describe all isomorphism classes of finitely generated Λ-modules, where Λ is any
complete local (commutative noetherian) ring whose category of modules of finite length …

In this paper we consider the asymptotic behavior of the ranks of the free modules in
resolutions of finitely generated modules, M, over a commutative noetherian ring, R. We …