The local cohomology modules of Matlis reflexive modules are almost cofinite
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- by Richard Belshoff, Susan Palmer Slattery and Cameron Wickham
- Proc. Amer. Math. Soc. 124 (1996), 2649-2654
- DOI: https://doi.org/10.1090/S0002-9939-96-03326-6
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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 $M=R$.References
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Bibliographic 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
- Received by editor(s): October 24, 1994
- Received by editor(s) in revised form: March 22, 1995
- Communicated by: Wolmer V. Vasconcelos
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 2649-2654
- MSC (1991): Primary 13D45, 13C99, 13C05
- DOI: https://doi.org/10.1090/S0002-9939-96-03326-6
- MathSciNet review: 1326995