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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
HARTSHORNE’S QUESTIONS AND WEAKLY COFINITENESS
Type
JournalPaper
Keywords
weakly Laskerian modules, weakly cofinite modules, Krull dimension, Local cohomology modules, Abelian category
Year
2020
Journal Mathematical Reports
DOI
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. The main purpose of this paper is to answer the Hartshorne's questions in the class of weakly Laskerian modules. It is shown that if s  1 is a positive integer such that Extj R(R=a;M) is weakly Laskerian for all j  s and the R-module Hia (M) is FD1 for all i < s, then the R-module Hia (M) is a-weakly co nite for all i < s. In addition, we show that the category of all a-weakly co nite FD1 R-modules is an Abelian subcategory of the category of all R-modules. Also, we prove that if Exti R(R=a;M) is weakly Laskerian for all i  dimM, then the R-module Exti R(N;M) is weakly Laskerian for all i  0 and for any nitely generated R-module N with SuppR(N)  V (a) and dimN  1. 1.