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Faltings' Finiteness Dimension of Local Cohomology Modules Over Local Cohen–Macaulay Rings

Published online by Cambridge University Press:  20 November 2018

Kamal Bahmanpour  and
Reza Naghipour
Kamal Bahmanpour
Affiliation:
Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, 56199-11367, Ardabil, Iran and School of Mathematics, Institute for Research in Fundamental Sciences (IPM), 19395-5746, Tehran, Iran. e-mail: [email protected]
Reza Naghipour
Affiliation:
Department of Mathematics, University of Tabriz, Tabriz, Iran and School of Mathematics, Institute for Research in Fundamental Sciences (IPM), 19395-5746, Tehran, Iran. e-mail: [email protected]
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Abstract

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Let $(R,\mathfrak{m})$ denote a local Cohen–Macaulay ring and $I$ a non-nilpotent ideal of $R$. The purpose of this article is to investigate Faltings’ finiteness dimension ${{f}_{I}}(R)$ and the equidimensionalness of certain homomorphic images of $R$. As a consequence we deduce that ${{f}_{I}}(R)=\max \{1,\text{ht}I\}$, and if $\text{mAs}{{\text{s}}_{R}}(R/I)$ is contained in $\text{As}{{\text{s}}_{R}}(R)$, then the ring $R/I+{{\bigcup }_{n\ge 1}}(0{{:}_{R}}{{I}^{n}})$ is equidimensional of dimension dim $R-1$. Moreover, we will obtain a lower bound for injective dimension of the local cohomology module $H_{I}^{\text{ht}I}(R)$, in the case where $(R,\mathfrak{m})$ is a complete equidimensional local ring.

Keywords

13D4514B15Cohen Macaulay ringequidimensional ringfiniteness dimensionlocal cohomology
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 60 , Issue 2 , 01 June 2017 , pp. 225 - 234
Copyright
Copyright © Canadian Mathematical Society 2017

References

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