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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
Minimaxness and Coartinianness of Local Homology Modules
Type
Presentation
Keywords
Minimax modules,Coartinian modules
Year
2019
Researchers Marziyeh Hatamkhani

Abstract

Let $R$ be a commutative Noetherian ring and $a$ an ideal of $R$. Let $A$ be an Artinian $R$- module. We introduce the notion of the $n$th Artinianness dimension of $A$ relative to $a$, $g_n^a(A)=inf\{g^{a R_{p}}(^p A): p\in Spec(R) \ \ \text{and} \ \ dim R/p\geq n\}$, for all $n\in\mathbb{N}_{0}$ and prove that $g_1^a(A)=inf\{i\in\mathbb{N}_0: H_i^a(A) \ \ \text{is not minimax}\}$, whenever $R$ is a complete semi-local ring. Moreover, in this situation we show that $Coass_R(H_{g_1^a(A)}^a(A))$ is a finite set.