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Keywords:
Bass numbers; generalized local cohomology modules; Matlis reflexive
Bass numbers; generalized local cohomology modules; Matlis reflexive
Summary:
Let $(R,\mathfrak m )$ be a complete local ring, $\mathfrak a $ an ideal of $R$ and $N$ and $L$ two Matlis reflexive $R$-modules with $\mathop{{\rm Supp}} (L)\subseteq V(\mathfrak a )$. We prove that if $M$ is a finitely generated $R$-module, then $\mathop{{\rm Ext}}\nolimits_R^i(L,H_{\mathfrak a }^j(M,N))$ is Matlis reflexive for all $i$ and $j$ in the following cases: (a) $\mathop{{\rm dim}} R/{\mathfrak a }=1$; (b) $\mathop{{\rm cd}} (\mathfrak a )=1$; where $\mathop{{\rm cd}} $ is the cohomological dimension of $\mathfrak a $ in $R$; (c) $\mathop{{\rm dim}} R\leq 2$. In these cases we also prove that the Bass numbers of $H_{\mathfrak a }^j(M,N)$ are finite.
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