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 …

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 …

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 …

Let I be an ideal of a commutative Noetherian local ring R, and M and N two finitely
generated modules. Let t be a positive integer. We mainly prove that (i) if HIi (M, N) is …

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 …

In this paper, we consider the openness of the P-locus of a finitely generated module over a
commutative noetherian ring in the case where P is each of the properties FID, Gor, Can …

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 …

We show that if M is a finitely generated module over a commutative Noetherian local ring R
and I is a dimension one ideal of R (ie, dim RI= 1), then the local cohomology modules HIi …

It is proved that a module M over a commutative noetherian ring R is injective if Ext _ R^ i
((R/\mathfrak p) _\mathfrak p, M)= 0 Ext R i ((R/p) p, M)= 0 holds for every i\geqslant 1 i⩾ 1 …

In this article, we prove the following generalization of a result of Hartshorne: Let (S, n) be a
regular local ring of dimension 4. Assume that x, y, u, v is a regular system of parameters for …