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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 minimaxness and coatomicness of local cohomology modules
Type
JournalPaper
Keywords
Local cohomology modules, Minimax modules, coatomic modules, Artinan modules, local-global principle
Year
2022
Journal Czechoslovak Mathematical Journal
DOI
Researchers Marziyeh Hatamkhani ، Hajar Roshan-Shekalgourabi

Abstract

Let R be a commutative Noetherian ring, I an ideal of R and M an R-module. We wish to investigate the relation between vanishing, finiteness, Artinianness, minimaxness and C-minimaxness of local cohomology modules. We show that if M is a minimax R-module, then the local-global principle is valid for minimaxness of local cohomology modules. Moreover, if Hi I (M) is minimax for all i ≥ n ≥ 1, then Hi I (M) is Artinian for i ≥ n. It is shown that if M is a C-minimax module over a local ring such that Hi I (M) are C-minimax modules for all i < n (respectively i ≥ n), where n ≥ 1, then they must be minimax. Consequently, a vanishing theorem is proved for local cohomology m