@article{article_504110, title={ON THE ASSOCIATED PRIMES OF THE d-LOCAL COHOMOLOGY MODULES}, journal={International Electronic Journal of Algebra}, volume={25}, pages={55–63}, year={2019}, DOI={10.24330/ieja.504110}, author={Rahimi-molaei, Z. and Payrovi, Sh. and Babaei, S.}, keywords={Associated primes,vanishing theorem,d-local cohomology module}, abstract={<div> <span style="font-size: 12.6px;">This paper is concerned to relationship between the sets of </span> </div> <div> <span style="font-size: 12.6px;">associated primes of the $d$-local cohomology modules and the </span> </div> <div> <span style="font-size: 12.6px;">ordinary local cohomology </span> </div> <div> <span style="font-size: 12.6px;"> modules.  Let $R$ be a commutative Noetherian local ring, $M$ an </span> </div> <div> <span style="font-size: 12.6px;">  $R$-module and $d, t$ two integers. We prove that </span> </div> <div> <span style="font-size: 12.6px;"> ${\rm Ass}(H^t_d(M))=\bigcup_{I\in \Phi} {\rm Ass}(H^t_I(M))$ whenever $H^i_d(M)=0$ for all </span> </div> <div> <span style="font-size: 12.6px;"> $i< t$ and $\Phi=\{I: I  \text{ is an ideal of}\  $R$ </span> </div> <div> <span style="font-size: 12.6px;"> \text{ with} \dim R/I\leq d \}$. We give some information about </span> </div> <div> <span style="font-size: 12.6px;"> the non-vanishing of the $d$-local cohomology modules. To be more precise, we prove that </span> </div> <div> <span style="font-size: 12.6px;">$H^i_d(R)\neq 0$ if and only if $i=n-d$ whenever  $R$ is a </span> </div> <div> <span style="font-size: 12.6px;">Gorenstein ring of dimension $n$. This result leads to an example which shows that ${\rm Ass}(H^{n-d}_d(R))$ </span> </div> <div> <span style="font-size: 12.6px;">is not necessarily a finite set. </span> </div>}, number={25}, publisher={Abdullah HARMANCI}