Artinianness of formal local cohomology modules

Shahram Rezaei

Commentationes Mathematicae Universitatis Carolinae (2019)

  • Volume: 60, Issue: 2, page 177-185
  • ISSN: 0010-2628

Abstract

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Let 𝔞 be an ideal of Noetherian local ring ( R , 𝔪 ) and M a finitely generated R -module of dimension d . In this paper we investigate the Artinianness of formal local cohomology modules under certain conditions on the local cohomology modules with respect to 𝔪 . Also we prove that for an arbitrary local ring ( R , 𝔪 ) (not necessarily complete), we have Att R ( 𝔉 𝔞 d ( M ) ) = Min V ( Ann R 𝔉 𝔞 d ( M ) ) .

How to cite

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Rezaei, Shahram. "Artinianness of formal local cohomology modules." Commentationes Mathematicae Universitatis Carolinae 60.2 (2019): 177-185. <http://eudml.org/doc/294855>.

@article{Rezaei2019,
abstract = {Let $\{\mathfrak \{a\}\}$ be an ideal of Noetherian local ring $(R,\{\mathfrak \{m\}\})$ and $M$ a finitely generated $R$-module of dimension $d$. In this paper we investigate the Artinianness of formal local cohomology modules under certain conditions on the local cohomology modules with respect to $\{\mathfrak \{m\}\}$. Also we prove that for an arbitrary local ring $(R,\{\mathfrak \{m\}\})$ (not necessarily complete), we have $\{\rm Att\}_R(\mathfrak \{F\}_\{\mathfrak \{a\}\}^d(M)) =\{\rm Min\} \{\rm V\}(\{\rm Ann\}_R \mathfrak \{F\}_\{\mathfrak \{a\}\}^d(M)).$},
author = {Rezaei, Shahram},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {formal local cohomology; local cohomology},
language = {eng},
number = {2},
pages = {177-185},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Artinianness of formal local cohomology modules},
url = {http://eudml.org/doc/294855},
volume = {60},
year = {2019},
}

TY - JOUR
AU - Rezaei, Shahram
TI - Artinianness of formal local cohomology modules
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2019
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 60
IS - 2
SP - 177
EP - 185
AB - Let ${\mathfrak {a}}$ be an ideal of Noetherian local ring $(R,{\mathfrak {m}})$ and $M$ a finitely generated $R$-module of dimension $d$. In this paper we investigate the Artinianness of formal local cohomology modules under certain conditions on the local cohomology modules with respect to ${\mathfrak {m}}$. Also we prove that for an arbitrary local ring $(R,{\mathfrak {m}})$ (not necessarily complete), we have ${\rm Att}_R(\mathfrak {F}_{\mathfrak {a}}^d(M)) ={\rm Min} {\rm V}({\rm Ann}_R \mathfrak {F}_{\mathfrak {a}}^d(M)).$
LA - eng
KW - formal local cohomology; local cohomology
UR - http://eudml.org/doc/294855
ER -

References

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  9. Rezaei S., 10.2996/kmj/1436403898, Kodai Math. J. 38 (2015), no. 2, 430–436. MR3368073DOI10.2996/kmj/1436403898
  10. Rezaei S., 10.1080/00927872.2016.1226867, Comm. Algebra 45 (2017), no. 5, 1935–1940. MR3582837DOI10.1080/00927872.2016.1226867
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