Local cohomology modules with infinite dimensional socles
Authors:
Thomas Marley and Janet C. Vassilev
Journal:
Proc. Amer. Math. Soc. 132 (2004), 3485-3490
MSC (2000):
Primary 13D45
DOI:
https://doi.org/10.1090/S0002-9939-04-07658-0
Published electronically:
July 22, 2004
MathSciNet review:
2084068
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: In this paper we prove the following generalization of a result of Hartshorne: Let be a commutative Noetherian local ring of dimension at least two,
, and
. Let
be a homogeneous element of
such that the coefficients of
form a system of parameters for
. Then the socle of
is infinite dimensional.
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Additional Information
Thomas Marley
Affiliation:
Department of Mathematics, University of Nebraska-Lincoln, Lincoln, Nebraska 68588-0323
Email:
tmarley@math.unl.edu
Janet C. Vassilev
Affiliation:
Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkan- sas 72701
Email:
jvassil@uark.edu
DOI:
https://doi.org/10.1090/S0002-9939-04-07658-0
Keywords:
Local cohomology
Received by editor(s):
July 16, 2003
Published electronically:
July 22, 2004
Additional Notes:
The first author was partially supported by NSF grant DMS-0071008.
Communicated by:
Bernd Ulrich
Article copyright:
© Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.