Let be an ideal of a commutative Noetherian ring R, and let M and N be finitely generated R-
modules. Let be the-finiteness dimension of N. In this paper, among other things, we show …

Let (R, m) denote an n-dimensional Gorenstein ring. For an ideal I⊂ R of height c we are
interested in the endomorphism ring B= HomR (HIc (R), HIc (R)). It turns out that B is a …

Let R be a commutative Noetherian ring and let M be a finite (that is, finitely generated) R-
module. The notion grade of M, grade M, has been introduced by Rees as the least integer …

Let R be a commutative noetherian henselian non-Gorenstein local ring of depth zero.
Denote by mod R the category of all finitely generated R-modules, and by the full …

R. Sazeedeh showed that top local cohomology modules are Gorenstein injective in a
Gorenstein local ring with at most two dimensions. In this paper, it is proved that the …

Let (R, m) denote an n-dimensional Gorenstein ring. For an ideal I⊂ R with gradeI= c we
define new numerical invariants τi, j (I) as the socle dimensions of Hmi (HIn− j (R)). In case of …

Given a one-dimensional Cohen-Macaulay local ring (R, m, k), we prove that it is almost
Gorenstein if and only if m is a canonical module of the ring m: m. Then, we generalize this …

Given a homomorphism of commutative noetherian rings R→ S and an S-module N, it is
proved that the Gorenstein flat dimension of N over R, when finite, may be computed locally …

Let R be a commutative Noetherian ring, α an ideal of R, and M, N two finitely generated R-
modules. We prove that the generalized local cohomology modules Ht α (M, N) are α …

We prove that if $ M $, $ N $ are finite modules over a Gorenstein local ring $ R $ of
codimension at most $4 $, then the vanishing of $\operatorname {Ext}^ n_R (M, N) $ for …