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

 

On endomorphism rings of local cohomology modules


Authors: M. Hellus and J. Stückrad
Journal: Proc. Amer. Math. Soc. 136 (2008), 2333-2341
MSC (2000): Primary 13C40; Secondary 13C05
Published electronically: March 13, 2008
MathSciNet review: 2390499
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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.


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Additional Information

M. Hellus
Affiliation: Universität Leipzig, Fakultät für Mathematik und Informatik, PF 10 09 20, D-04009, Leipzig, Germany
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

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09240-X
PII: S 0002-9939(08)09240-X
Keywords: Local cohomology, endomorphism ring, Matlis dual, complete intersection
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
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.