Finiteness of local homology modules

Shahram Rezaei

Archivum Mathematicum (2020)

  • Volume: 056, Issue: 1, page 31-41
  • ISSN: 0044-8753

Abstract

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Let be an ideal of Noetherian ring and a finitely generated -module. In this paper, we introduce the concept of weakly colaskerian modules and by using this concept, we give some vanishing and finiteness results for local homology modules. Let , we will prove that for any integer

If N is a weakly colaskerian linearly compact R -module such that (0:_N {I_M})\ne 0 then

\operatorname{width}_{I_M}(N)= \inf \lbrace i\mid \operatorname{H}_i^{I_M}(N)\ne 0 \rbrace =\inf \lbrace i \mid \operatorname{H}_i^I(M,N)\ne 0 \rbrace \,.

If (R,\mathfrak {m}) is a Noetherian local ring and N is an artinian R -module then

\cup _{i<n}\operatorname{Cos}_R\big (\operatorname{H}_i^{I_M}(N)\big )=\cup _{i<n}\operatorname{Cos}_R\big (\operatorname{H}_i^I(M,N)\big )=\\ \cup _{i<n}\operatorname{Cos}_R\big (\operatorname{Tor}_i^R(M/IM,N)\big )\,,

\inf \lbrace i \mid \operatorname{H}_i^{I_M}(N) \text{ is not Noetherian $R$-module\,} \rbrace =\\ \inf \lbrace i \mid \operatorname{H}_i^I(M,N) \mbox {\ is not Noetherian R-module\,}\rbrace \,.

How to cite

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Rezaei, Shahram. "Finiteness of local homology modules." Archivum Mathematicum 056.1 (2020): 31-41. <http://eudml.org/doc/295083>.

@article{Rezaei2020,
abstract = {Let $I$ be an ideal of Noetherian ring $R$ and $M$ a finitely generated $R$-module. In this paper, we introduce the concept of weakly colaskerian modules and by using this concept, we give some vanishing and finiteness results for local homology modules. Let $I_\{M\}:=\operatorname\{Ann\}_\{R\}(M/IM)$, we will prove that for any integer $n$},
author = {Rezaei, Shahram},
journal = {Archivum Mathematicum},
keywords = {coregular sequence; local homology; weakly colaskerian},
language = {eng},
number = {1},
pages = {31-41},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Finiteness of local homology modules},
url = {http://eudml.org/doc/295083},
volume = {056},
year = {2020},
}

TY - JOUR
AU - Rezaei, Shahram
TI - Finiteness of local homology modules
JO - Archivum Mathematicum
PY - 2020
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 056
IS - 1
SP - 31
EP - 41
AB - Let $I$ be an ideal of Noetherian ring $R$ and $M$ a finitely generated $R$-module. In this paper, we introduce the concept of weakly colaskerian modules and by using this concept, we give some vanishing and finiteness results for local homology modules. Let $I_{M}:=\operatorname{Ann}_{R}(M/IM)$, we will prove that for any integer $n$
LA - eng
KW - coregular sequence; local homology; weakly colaskerian
UR - http://eudml.org/doc/295083
ER -

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