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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
COLOCALIZATION OF GENERALIZED LOCAL HOMOLOGY MODULES
Type
JournalPaper
Keywords
Colocalization, generalized local homology modules, representable modules.
Year
2022
Journal Bulletin of the Korean Mathematical Society
DOI
Researchers Marziyeh Hatamkhani

Abstract

Let R be a commutative Noetherian ring and I an ideal of R. In this paper, we study colocalization of generalized local homology modules. We intend to establish a dual case of local-global principle for the niteness of generalized local cohomology modules. Let M be a nitely generated R-module and N a representable R-module. We introduce the notions of the representation dimension rI (M;N) and artinianness dimension aI (M;N) of M;N with respect to I by rI (M;N) = inffi 2 N0 : HI i (M;N) is not representableg and aI (M;N) = inffi 2 N0 : HI i (M;N) is not artiniang and we show that aI (M;N) = rI (M;N) = inffrIRp (Mp;p N) : p 2 Spec(R)g  inffaIRp (Mp;p N) : p 2 Spec(R)g. Also, in the case where R is semi-local and N a semi discrete linearly compact R-module such that N= T t>0 ItN is artinian we prove that inffi : HI i (M;N) is not minimaxg=inffrIRp (Mp;p N) : p 2 Spec(R)nMax(R)g: 1. Introduction