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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The local cohomology modules of Matlis reflexive modules are almost cofinite


Authors: Richard Belshoff, Susan Palmer Slattery and Cameron Wickham
Journal: Proc. Amer. Math. Soc. 124 (1996), 2649-2654
MSC (1991): Primary 13D45, 13C99, 13C05
MathSciNet review: 1326995
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Abstract: We show that if $M$ and $N$ are Matlis reflexive modules over a complete Gorenstein local domain $R$ and $I$ is an ideal of $R$ such that the dimension of $R/I$ is one, then the modules $\mathrm {Ext}^{i}_{R}(N,\mathrm {H}^{j}_{I}(M))$ are Matlis reflexive for all $i$ and $j$ if $\mathrm {Supp}(N) \subseteq V(I)$. It follows that the Bass numbers of $\mathrm {H}^{j}_{I}(M)$ are finite. If $R$ is not a domain, then the same results hold for $M=R$.


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Additional Information

Richard Belshoff
Affiliation: Department of Mathematics, Southwest Missouri State University, Springfield, Missouri 65804
Email: rgb865f@cnas.smsu.edu

Susan Palmer Slattery
Address at time of publication: S. P. Slattery: Department of Mathematics, Alabama State University, Montgomery, Alabama 36101
Email: slattery@asu.alasu.edu

Cameron Wickham
Affiliation: Department of Mathematics, Southwest Missouri State University, Springfield, Missouri 65804
Email: cgw121f@cnas.smsu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03326-6
PII: S 0002-9939(96)03326-6
Keywords: Matlis reflexive module, local cohomology module, Gorenstein ring, Bass number
Received by editor(s): October 24, 1994
Received by editor(s) in revised form: March 22, 1995
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1996 American Mathematical Society