8 citations · 23 across the 12 of their papers we have counts for
9 papers · 1 filter
-Cohen Macaulay modules
Waqas Mahmood, Maria Azam
A finitely generated module over a commutative Noetherian ring is called an -Cohen Macaulay module, if \[ \grade(I,M) + \dim(M/IM)= \dim(M), \] where is a proper ide…
On generalized completion homology modules
Waqas Mahmood
Let be an ideal of a commutative Noetherian ring . Let and be any -modules. We define the generalized completion homology modules , for $i\in \mathb…
Cohomologically complete intersections with vanishing of Betti numbers
Waqas Mahmood
Let be ideal of an -dimensional local Gorenstein ring . In this paper we will describe several necessary and sufficient conditions such that the ideal becomes cohomol…
On natural homomorphisms of local cohomology modules
Waqas Mahmood
Let be a non-zero finitely generated module over a finite dimensional commutative Noetherian local ring with dim. Let be an ideal of with gr…
A Note on Endomorphisms of Local Cohomology Modules
Waqas Mahmood, Zohaib Zahid
Let denote an ideal of a local ring of dimension . Let denote a finitely generated -module. We study the endomorphism ring of the local cohomology…
On Cohomologically Complete Intersections in Cohen-Macaulay Rings
Waqas Mahmood
An ideal I of a local Cohen-Macaulay ring R is called a cohomologically complete intersection if H^i_I(R) = 0 for all i \neq c = height(I). Here H^i_I(R), i \in Z denotes the local…
A Few Comments On Matlis Duality
Waqas Mahmood
For a Noetherian local ring with $\mathfrak p\in \Spec(R)$ we denote by the -injective hull of . We will show that it has…
On Invariants and Endomorphism Rings of Local Cohomology Modules
Waqas Mahmood, Peter Schenzel
Let denote an -dimensional Gorenstein ring. For an ideal with $\grade I = c$ we define new numerical invariants as the socle dimens…
On Endomorphism Rings of Local Cohomology Modules
Waqas Mahmood
Let I be an ideal of a Complete Cohen-Macaulay local ring R of dimension n. We wil show that the natural homomorphism Rto HomR(HcI(KR), HcI(KR)) is an isomorphism provided that I i…