Geodesic
Bass Numbers of Generalized Local Cohomology Modules
Publications de l'Institut Mathématique, _N_S_97 (2015) no. 111, p. 233 .

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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 $\sum_{j=0}^t\mu^r\big(\frak p,\operatorname{Ext}^{t-j}_R(M, H^j_I(N))\big)$. A corollary is that $ \operatorname{Ass}\big(H_I^t(M,N)\big)\subseteq \bigcup_{j=0}^t\operatorname{Ass}\big(\operatorname{Ext}^{t-j}_R(M,H^j_I(N))\big). $ In a slightly different direction, we also present some well known results about generalized local cohomology modules.
DOI : 10.2298/PIM140620001P
Classification : 13D45 14B15
Keywords: generalized local cohomology, Bass numbers 
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     title = {Bass {Numbers} of {Generalized} {Local} {Cohomology} {Modules}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {233 },
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Sh. Payrovi; S. Babaei; I. Khalili-Gorji. Bass Numbers of Generalized Local Cohomology Modules. Publications de l'Institut Mathématique, _N_S_97 (2015) no. 111, p. 233 . doi : 10.2298/PIM140620001P. http://geodesic.mathdoc.fr/articles/10.2298/PIM140620001P/

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