Let $(R,\mathfrak m) $ denote an $ n $-dimensional complete local Gorenstein ring. For an
ideal $ I $ of $ R $ let $ H^ i_I (R), i\in\mathbb Z, $ denote the local cohomology modules of …

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 …

Let A be a commutative ring, and let I be an ideal of A. The cohomological dimension ofl in
A, denoted by cd (A, I), is the smallest integer n such that the local cohomology modules …

Let 𝔞 be an ideal of a commutative Noetherian ring R and M and N two finitely generated R-
modules. Let cd𝔞 (M, N) denote the supremum of the i's such that. First, by using the theory …

On Vanishing of Generalized Local Cohomology Modules Page 1 Algebra Colloquium c© 2005
AMSS CAS & SUZHOU UNIV Algebra Colloquium 12:2 (2005) 213–218 On Vanishing of …

Let (R, 𝔪) be a commutative Noetherian local ring and M an R-module which is relative
Cohen-Macaulay with respect to a proper ideal 𝔞 of R, and set n:= ht M𝔞. We prove that …

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 …

An ideal I of a local Gorenstein ring (R, m) is called cohomologically complete intersection
whenever HIi (R)= 0 for all i≠ heightI. Here HIi (R), i∈ Z, denotes the local cohomology of R …

In this paper we assume that $ R $ is a Gorenstein Noetherian ring. We show that if
$(R,\mathfrak {m}) $ is also a local ring with Krull dimension $ d $ that is less than or equal to …

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 …