Local cohomology modules with infinite dimensional socles

Marley, Thomas; Vassilev, Janet

doi:10.1090/S0002-9939-04-07658-0

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
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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, $R=T[x_1,\dots,x_n]$ , and $I=(x_1,\ldots,x_n)$ . 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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