Extension functors of generalized local cohomology modules

Abstract

Let $R$ be a commutative Noetherian ring with non-zero identity, $\mathfrak{a}$ an ideal of $R$, $M$ a finitely generated $R$--module, and $X$ an arbitrary $R$--module. In this paper, for non-negative integers $s,t$ and a finitely generated $R$--module $N$, we study the membership of ${\mathrm{Ext}}_R^s(N,H_{\mathfrak{a}}^t(M,X))$ in Serre subcategories of the category of $R$--modules and present some upper bounds for the injective dimension and the Bass numbers of $H_{\mathfrak{a}}^t(M,X)$. We also give some results on cofiniteness and minimaxness of $H_{\mathfrak{a}}^t(M,X)$ and finiteness of ${\mathrm{Ass}}_R(H_{\mathfrak{a}}^t(M,X)$.

16 pages