Let $ R $ be a commutative Noetherian ring of prime characteristic $ p $. In this paper, we
give a short proof using filter regular sequences that the set of associated prime ideals of …

Let 𝔞, 𝔟 be ideals of a commutative Noetherian ring R and N be a finitely generated R-
module. By using filter regular sequences, we show that the infimum of integers i such that …

Let $\mathfrak {a} $ be an ideal of a commutative Noetherian ring $ R $ and $ M $ a finitely
generated $ R $-module. Let $ t $ be a natural integer. It is shown that there is a finite subset …

Let $ R $ be a Noetherian ring, $\mathfrak a $ be an ideal of $ R $ and $ M $ be a finitely
generated $ R $-module. The aim of this paper is to show that if $ t $ is the least integer such …

Let $ A $ be a Noetherian local ring of dim $ A= n $ and $\mathfrak {m} $ the maximal ideal
of $ A $. Let $ H_ {u}^{i}(\cdot) $ stand for the $ i^{th} $ local cohomology functor relative to …

Let R be a commutative F-algebra, where F is a field of characteristic 0, satisfying the
following conditions: R is equidimensional of dimension n, every residual field with respect …

Let $\fa $ denote an ideal of a commutative Noetherian ring $ R $ and $ M $ and $ N $ two
finitely generated $ R $-modules with $\pd M<\infty $. It is shown that if $\fa $ is principal or …

Let $ R= k [x_1,\cdots, x_n] $ be a polynomial ring over a field $ k $ of characteristic $ p> 0, $
and let $ I=(f_1,\cdots, f_s) $ be an ideal of $ R. $ We prove that every associated prime $ P …

This article is a study of the local cohomology module in the case that R is a commutative
Noetherian ring containing a field and is a monomial ideal in a R-sequence. We will …

In this article, we prove the following generalization of a result of Hartshorne: Let (S, n) be a
regular local ring of dimension 4. Assume that x, y, u, v is a regular system of parameters for …