On the Local Cohomology and Formal Local Cohomology Modules

Shahram Rezaei; Behruz Sadeghi

doi:10.5666/KMJ.2022.63.1.37

Article

Kyungpook Mathematical Journal 2023; 63(1): 37-43

Published online March 31, 2023

On the Local Cohomology and Formal Local Cohomology Modules

Shahram Rezaei^* and Behruz Sadeghi

Department of Mathematics, Payame Noor University (PNU), Tehran, Iran
e-mail : sha.rezaei@gmail.com and b-sadeqi@student.pnu.ac.ir

Received: July 31, 2022; Revised: November 20, 2023; Accepted: January 17, 2023

Abstract

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Abstract

Let 𝔞 and 𝔟 be ideals of a commutative Noetherian ring R and M be a finitely generated R-module of dimension d>0. We prove some results concerning the top local cohomology and top formal local cohomology modules. Among other things, we determine SuppR(𝔟H𝔞d(M)) and SuppR(𝔟F𝔞d(M)). Also, we obtain some relations between AnnR(𝔟H𝔞d(M)), AttR(𝔟H𝔞d(M)) and SuppR(𝔟H𝔞d(M)) and we get similar results for 𝔟F𝔞d(M).

Keywords: formal local cohomology, local cohomology