Publications de l'Institut Mathématique, Nouvelle Série Vol. 97(111), pp. 233–238 (2015) 

BASS NUMBERS OF GENERALIZED LOCAL COHOMOLOGY MODULESSh. Payrovi, S. Babaei, I. KhaliliGorjiDepartment of Mathematics, Imam Khomeini International University, Qazvin, IranAbstract: Let $R$ be a Noetherian ring, $M$ a finitely generated $R$module and $N$ an arbitrary $R$module. We consider the generalized local cohomology modules, with respect to an arbitrary ideal $I$ of $R$, and prove that, for all nonnegative integers $r,t$ and all $\frak p\in\operatorname{Spec}(R)$ the Bass number $\mu^r(\frak p,H^t_I(M,N))$ is bounded above by $\sum_{j=0}^t\mu^r\big(\frak p,\operatorname{Ext}^{tj}_R(M, H^j_I(N))\big)$. A corollary is that $ \operatorname{Ass}\big(H_I^t(M,N)\big)\subseteq \bigcup_{j=0}^t\operatorname{Ass}\big(\operatorname{Ext}^{tj}_R(M,H^j_I(N))\big). $ In a slightly different direction, we also present some well known results about generalized local cohomology modules. Keywords: generalized local cohomology, Bass numbers Classification (MSC2000): 13D45; 14B15 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 16 Apr 2015. This page was last modified: 21 Apr 2015.
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