2024 : 6 : 13
Marziyeh Hatamkhani

Marziyeh Hatamkhani

Academic rank: Assistant Professor
ORCID: https://orcid.org/0000-0003-1021-2827
Education: PhD.
ScopusId: 55647016200
Faculty: Science
Address: Arak University
Phone:

Research

Title
ON THE WEAKLY COFINITENESS OF LOCAL COHOMOLOGY MODULES
Type
Presentation
Keywords
weakly Laskerian modules, weakly cofinite modules, Krull dimension, Local cohomology modules, Abelian category
Year
2023
Researchers Hajar Roshan-Shekalgourabi ، Marziyeh Hatamkhani

Abstract

Let R be a commutative Noetherian ring, a be an ideal of R and M be an R-module. In this article, we investigate the cofiniteness and weakly cofiniteness of local cohomology and generalized local cohomology modules. Among other things, we prove that if Exti R(R/a, M) is weakly Laskerian for all i ≤ dim M, then the R-module Exti R(N, M) is weakly Laskerian for all i ≥ 0 and for any finitely generated R-module N with SuppR(N) ⊆ V (a) and dim N ≤ 1. As a consequence, we show that if M is an Rmodule such that Hi a (M) is a-weakly cofinite for all i ≥ 0, then the R-module Hi a (N, M) is weakly Laskerian for all i ≥ 0 and for any finitely generated R-module N with SuppR(N) ⊆ V (a) and dim N ≤ 1.