3 edited title; edited title; edited title

2 edited title

1

# b-cofiniteness of Ext mohules applied to a-cohomology modules

Assume that $n,j$ are non-negative integers; $a,b$ ideals of a Noetherian ring $R$ such that $a\subseteq b$ and $M$ a finte $R$-module of dimension $d$. If the following two conditions hold:

(I) For each $t=1,\dots,n$ the $R$-modules $Ext^{j+t+1}_R(\frac{R}{b},H^{n-1}_a(M))$ are finite

(II) For each $t=1,\dots,d-n$ the $R$-modules $Ext^{j-t-1}_R(\frac{R}{b},H^{n+t}_a(M))$ are finite Then can we deduce that $Ext^j_R(\frac{R}{b},H^{n}_a(M))$ is finite? If yes, This can be a generalization of a result in the paper "Associated Primes of the Local Cohomology Modules" by Dibaei & Yasemi