Let R be a d-dimensional Cohen–Macaulay (CM) local ring of minimal multiplicity. Set S:=
R/(f), where f:= f1,..., fc is an R-regular sequence. Suppose M and N are maximal CM S …

Let (R, m) be a Noetherian local ring which is a homomorphic image of a local Gorenstein
ring and let M be a finitely generated R-module of dimension d> 0. According to Schenzel …

Let R be a Cohen–Macaulay local ring. We prove that the n th syzygy module of a maximal
Cohen–Macaulay R-module cannot have a semidualizing direct summand for every n≥ 1 …

In this paper, we will study the local cohomology modules HiI (S) of a polynomial ring S= k
[x1,…, xn] with supports in a (radical) monomial ideal I. When S/I is a Cohen–Macaulay ring …

Let S be a Gorenstein local ring and suppose that M is a finitely generated Cohen–Macaulay
S-module of codimension c. Given a regular sequence f1,..., fc in the annihilator of M we set …

Let M be a finitely generated module over a commutative noetherian ring A (with 1). Then M
is called qtcusi-perfect if G-dim M= gradeM. Perfect modules (ie projective dimension …

Let $(R,\frak m) $ be a homomorphic image of a Cohen-Macaulay local ring and $ M $ a
finitely generated $ R $-module. We use the splitting of local cohomology to shed a new light …

This paper contains two theorems concerning the theory of maximal Cohen–Macaulay
modules. The first theorem proves that certain Ext groups between maximal Cohen …

Let M be a finite module over a commutative noetherian ring R. For ideals a and b of R, the
relations between cohomological dimensions of M with respect to a, b, a∩ b and a+ b are …

We study the vanishing of some Tori (M, R/J) when R is a local Cohen–Macaulay ring, J any
ideal of R with R/J Cohen–Macaulay and M a finitely generated R-module. We use this …