Matlis reflexive and generalized local cohomology modules |
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| Authors: | Amir Mafi |
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| Affiliation: | (1) Faculty of Mathematical Sciences, Teacher Training University, Tehran, Iran;(2) Institute for Theoretical Physics and Mathematics (IPM), Tehran, Iran;(3) Center of Excellence in Biomathematics, School of Mathematics, University of Tehran, P.O. Box 13145-448, Tehran, Iran |
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| Abstract: | Let (R,m) be a complete local ring, a an ideal of R and N and L two Matlis reflexive R-modules with Supp(L) ⊆ V(a). We prove that if M is a finitely generated R-module, then Exti R i (L, H a j (M,N)) is Matlis reflexive for all i and j in the following cases: | (a) | dim R/a = 1 | | (b) | cd(a) = 1; where cd is the cohomological dimension of a in R | | (c) | dim R ⩽ 2. | In these cases we also prove that the Bass numbers of H a j (M, N) are finite. |
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