Let $ R $ be a commutative Noetherian ring with non-zero identity, $\fa $ an ideal of $ R $,
and $ X $ an $ R $--module. In this paper, for fixed integers $ s, t $ and a finite $\fa $--torsion …

Let $ R $ be a commutative Noetherian ring with non-zero identity, $\mathfrak {a} $ and
$\mathfrak {b} $ ideals of $ R $ with $\mathfrak {a}\subseteq\mathfrak {b} $, and $ M $ a …

Let R be a commutative Noetherian ring with nonzero identity, 𝔞 an ideal of R, M a finite R–
module, X an arbitrary R–module, and na non-negative integer. Here, we show that, in the …

Let (R,m) be a complete Noetherian local ring, I a proper ideal of R and M, N two finitely
generated R-modules such that Supp (N)⊆V(I). Let t≧0 be an integer such that for each …

Abstract‎ Let $ n $ be a non-negative integer‎,‎ $ R $ a commutative Noetherian ring with $\dim
(R)\leq n‎+‎ 2$‎,‎ $\mathfrak {a} $ an ideal of $ R $‎,‎ and $ X $ an arbitrary $ R $-module‎.‎ In this …

Let $ n $ be a non-negative integer, $ R $ a commutative Noetherian ring, $\mathfrak {a} $
an ideal of $ R $, $ M $ a finitely generated $ R $-module, and $ X $ an arbitrary $ R …

Let R be a Noetherian ring and I an ideal of R. Let M be an I-cofinite and N a finitely
generated R-module. It is shown that the R-modules $ Tor_ {i}^{R}(N, M) $ are I-cofinite for …

Finiteness of Extension Functors of Local Cohomology Modules Page 1 Communications in
Algebra®, 34: 3097–3101, 2006 Copyright © Taylor & Francis Group, LLC ISSN: 0092-7872 …

Let I be an ideal of a commutative Noetherian ring R. It is shown that the R-modules HI j (M)
are I-cofinite for all finitely generated R-modules M and all j∈ ℕ0 if and only if the R …

Let a be an ideal of a commutative Noetherian (not necessarily local) ring R. In the case cd
(a, R)≤ 1, we show that the subcategory of a-cofinite R-modules is Abelian. Using this fact …