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Melkersson condition on Serre subcategories

100%

Sazeedeh R., Rasuli R.

Colloquium Mathematicum

2016

tom 144

nr 2

289-300

Let R be a commutative noetherian ring, let 𝔞 be an ideal of R, and let 𝓢 be a subcategory of the category of R-modules. The condition $C_{𝔞}$, defined for R-modules, was introduced by Aghapournahr and Melkersson (2008) in order to study when the local cohomology modules relative to 𝔞 belong to 𝓢. In this paper, we define and study the class $𝓢_{𝔞}$ consisting of all modules satisfying $C_{𝔞}$. If 𝔞 and 𝔟 are ideals of R, we get a necessary and sufficient condition for 𝓢 to satisfy $C_{𝔞}$ and $C_{𝔟}$ simultaneously. We also find some sufficient conditions under which 𝓢 satisfies $C_{𝔞}$. As an application, we investigate when local cohomology modules lie in a Serre subcategory.

Cofiniteness of generalized local cohomology modules

100%

Divaani-Aazar K., Sazeedeh R.

Colloquium Mathematicum

2004

tom 99

nr 2

283-290

Let 𝔞 denote an ideal of a commutative Noetherian ring R, and M and N two finitely generated R-modules with pd M < ∞. It is shown that if either 𝔞 is principal, or R is complete local and 𝔞 is a prime ideal with dim R/𝔞 = 1, then the generalized local cohomology module $H^i_{𝔞}(M,N)$ is 𝔞-cofinite for all i ≥ 0. This provides an affirmative answer to a question proposed in [13].

Ograniczanie wyników

2 Colloquium Mathematicum

2 Sazeedeh R.

1 Divaani-Aazar K.

1 Rasuli R.

1 2016

1 2004

Wyniki wyszukiwania

Melkersson condition on Serre subcategories

Cofiniteness of generalized local cohomology modules