On endomorphism rings of local cohomology modules
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- by M. Hellus and J. Stückrad
- Proc. Amer. Math. Soc. 136 (2008), 2333-2341
- DOI: https://doi.org/10.1090/S0002-9939-08-09240-X
- Published electronically: March 13, 2008
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Abstract:
Let $R$ be a local complete ring. For an $R$-module $M$ the canonical ring map $R\to \mathrm {End}_R(M)$ is in general neither injective nor surjective; we show that it is bijective for every local cohomology module $M:=H^h_I(R)$ if $H^l_I(R)=0$ for every $l\neq h$ $(=\mathrm {height} (I))$ ($I$ an ideal of $R$); furthermore the same holds for the Matlis dual of such a module. As an application we prove new criteria for an ideal to be a set-theoretic complete intersection.References
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Bibliographic Information
- M. Hellus
- Affiliation: Universität Leipzig, Fakultät für Mathematik und Informatik, PF 10 09 20, D-04009, Leipzig, Germany
- MR Author ID: 674206
- Email: hellus@math.uni-leipzig.de
- J. Stückrad
- Affiliation: Universität Leipzig, Fakultät für Mathematik und Informatik, PF 10 09 20, D-04009, Leipzig, Germany
- Email: stueckrad@math.uni-leipzig.de
- Received by editor(s): February 21, 2007
- Received by editor(s) in revised form: April 19, 2007
- Published electronically: March 13, 2008
- Communicated by: Bernd Ulrich
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 2333-2341
- MSC (2000): Primary 13C40; Secondary 13C05
- DOI: https://doi.org/10.1090/S0002-9939-08-09240-X
- MathSciNet review: 2390499