Modules with minimax Cousin cohomologies

Let R be a commutative Noetherian ring with non-zero identity and let X be an arbitrary R-module. In this paper, we show that if all the cohomology modules of the Cousin complex for X are minimax, then the following hold for any prime ideal p of R and for every integer n less than X—the height of p:...

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Published in:Algebra and Discrete Mathematics
Date:2020
Main Author: Vahidi, A.
Format: Article
Language:English
Published: Інститут прикладної математики і механіки НАН України 2020
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/188558
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Modules with minimax Cousin cohomologies / A. Vahidi // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 1. — С. 143–149. — Бібліогр.: 16 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Vahidi, A.
author_facet Vahidi, A.
citation_txt Modules with minimax Cousin cohomologies / A. Vahidi // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 1. — С. 143–149. — Бібліогр.: 16 назв. — англ.
collection DSpace DC
container_title Algebra and Discrete Mathematics
description Let R be a commutative Noetherian ring with non-zero identity and let X be an arbitrary R-module. In this paper, we show that if all the cohomology modules of the Cousin complex for X are minimax, then the following hold for any prime ideal p of R and for every integer n less than X—the height of p: (i) the nth Bass number of X with respect to p is finite; (ii) the nth local cohomology module of Xp with respect to pRp is Artinian.
first_indexed 2025-11-24T09:25:50Z
format Article
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id nasplib_isofts_kiev_ua-123456789-188558
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1726-3255
language English
last_indexed 2025-11-24T09:25:50Z
publishDate 2020
publisher Інститут прикладної математики і механіки НАН України
record_format dspace
spelling Vahidi, A.
2023-03-05T17:40:08Z
2023-03-05T17:40:08Z
2020
Modules with minimax Cousin cohomologies / A. Vahidi // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 1. — С. 143–149. — Бібліогр.: 16 назв. — англ.
1726-3255
DOI:10.12958/adm528
2010 MSC: 13D02, 13D03, 13D45, 13E10.
https://nasplib.isofts.kiev.ua/handle/123456789/188558
Let R be a commutative Noetherian ring with non-zero identity and let X be an arbitrary R-module. In this paper, we show that if all the cohomology modules of the Cousin complex for X are minimax, then the following hold for any prime ideal p of R and for every integer n less than X—the height of p: (i) the nth Bass number of X with respect to p is finite; (ii) the nth local cohomology module of Xp with respect to pRp is Artinian.
This research was in part supported by a grant from Payame Noor University
en
Інститут прикладної математики і механіки НАН України
Algebra and Discrete Mathematics
Modules with minimax Cousin cohomologies
Article
published earlier
spellingShingle Modules with minimax Cousin cohomologies
Vahidi, A.
title Modules with minimax Cousin cohomologies
title_full Modules with minimax Cousin cohomologies
title_fullStr Modules with minimax Cousin cohomologies
title_full_unstemmed Modules with minimax Cousin cohomologies
title_short Modules with minimax Cousin cohomologies
title_sort modules with minimax cousin cohomologies
url https://nasplib.isofts.kiev.ua/handle/123456789/188558
work_keys_str_mv AT vahidia moduleswithminimaxcousincohomologies