IJPAM: Volume 99, No. 4 (2015)

RESULTS OF GENERALIZED LOCAL COHOMOLOGY
WITH RESPECT TO A PAIR OF IDEALS

Fatemeh Dehghani-Zadeh
Department of Mathematics
Islamic Azad University
Yazd Branch, Yazd, IRAN


Abstract. Let $(I,J)$ be a pair of ideals of a commutative Noetherian local ring $R$, and $M$ a finitely generated module. Let $t$ be a positive integer. We prove that $(i)$ if $H^{i}_{I,J}(M)$ is minimax for all $i<t$, then $H^{i}_{I,J}(M)$ is $(I,J)$-cofinite for all $i<t$ and $\hbox{Hom}\big(R/I, H^{t}_{I,J}(M)\big)$ is finitely generated; $(ii)$ if $\fa \in \widetilde{W}(I,J)$ and $H^{i}_{I,J}(M)$ is minimax for all $i<t$, then $\hbox{Ext}^{i}_{R}(R/\fa, T)$ is minimax for all $i<t$. We also prove that if $\hbox{Supp}H^{i}_{I,J}(M)=\{\fm\}$ for all $i<t$, then $H^{i}_{I,J}(M)$ is Artinian and $(I,J)$-cofinite for all $i<t$.

Received: October 22, 2014

AMS Subject Classification: 13D45, 13E05, 14B15

Key Words and Phrases: local cohomology modules, artinian modules, cofinite modules

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DOI: 10.12732/ijpam.v99i4.7 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 99
Issue: 4
Pages: 471 - 476


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