Volume 9, Issue 2 (11-2014)                   IJMSI 2014, 9(2): 7-13 | Back to browse issues page


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Pour Eshmanan Talemi A, Tehranian A. Local Cohomology with Respect to a Cohomologically Complete Intersection Pair of Ideals. IJMSI. 2014; 9 (2) :7-13
URL: http://ijmsi.ir/article-1-640-en.html
Abstract:  

Let $(R,fm,k)$ be a local Gorenstein ring of dimension $n$. Let $H_{I,J}^i(R)$ be the  local cohomology with respect to a pair of ideals $I,J$ and $c$ be the $inf{i|H_{I,J}^i(R)neq0}$. A pair of ideals $I, J$ is called cohomologically complete intersection if $H_{I,J}^i(R)=0$ for all $ineq c$. It is shown that, when $H_{I,J}^i(R)=0$ for all $ineq c$, (i) a minimal injective resolution of $H_{I,J}^c(R)$ presents like that of a Gorenstein ring (ii) $Hom_R(H_{I,J}^c(R),H_{I,J}^c(R))simeq R$, where $(R,fm)$ is a complete ring. Also we get an estimate of the  dimension of $H_{I,J}^i(R)$.

Type of Study: Research paper | Subject: General

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