We provide a formula (see Theorem 1.5) for the Matlis dual of the injective hull of R/p where
p is a one dimensional prime ideal in a local complete Gorenstein domain (R, m). This is …

The goal of this paper is twofold; on the one hand, motivated by questions raised by
Schenzel, we explore situations where the Hartshorne--Lichtenbaum Vanishing Theorem for …

Let $ I $ be ideal of an $ n $-dimensional local Gorenstein ring $ R $. In this paper we will
describe several necessary and sufficient conditions such that the ideal $ I $ becomes …

In this paper, several necessary and sufficient conditions are presented for a module M to be
cohomologically complete intersection module with respect to I, ie H_I^i(M)=0 for all …

Let $ I $ be an ideal of a commutative Noetherian ring $ R $. Let $ M $ and $ N $ be any $ R
$-modules. We define the generalized completion homology modules $ L_i\Lambda^ I (N …

Let $ M $ be a non-zero finitely generated module over a finite dimensional commutative
Noetherian local ring $(R,\mathfrak {m}) $ with dim $ _R (M)= t $. Let $ I $ be an ideal of $ R …

Let aa, I, J be ideals of a Noetherian local ring (R, m, k)(R, m, k). Let M and N be finitely
generated R-modules. We give a generalized version of the Duality Theorem for Cohen …

This work develops the theories of local cohomology and local homology with respect to an
arbitrary set of ideals and generalises most of the important results from the classical …