Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2016; 53(5): 1341-1352

Online first article August 25, 2016      Printed September 30, 2016

https://doi.org/10.4134/BKMS.b150632

Copyright © The Korean Mathematical Society.

Cofiniteness of general local cohomology modules for small dimensions

Moharram Aghapournahr and Kamal Bahmanpour

Arak University, University of Mohaghegh Ardabili

Abstract

Let $R$ be a commutative Noetherian ring, $\Phi$ a system of ideals of $R$ and $I\in \Phi$. In this paper among other things we prove that if $M$ is finitely generated and $t\in \mathbb{N}$ such that the $R$-module $\lc^{i}_\Phi(M)$ is ${\rm FD_{\leq 1}}$ (or weakly Laskerian) for all $i

Keywords: local cohomology, weakly Laskerian modules, ${\rm FD_{\leq n}}$ modules, cofinite modules, $ETH$-cofinite modules

MSC numbers: 13D45, 13E05, 14B15