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

 

A class of Hilbert series and the strong Lefschetz property


Author: Melissa Lindsey
Journal: Proc. Amer. Math. Soc. 139 (2011), 79-92
MSC (2010): Primary 13A02; Secondary 13C05
Published electronically: July 1, 2010
MathSciNet review: 2729072
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Abstract: We determine the class of Hilbert series $ \mathcal H$ so that if $ M$ is a finitely generated zero-dimensional $ R$-graded module with the strong Lefschetz property, then $ M\otimes_k k[y]/(y^m)$ has the strong Lefschetz property for an indeterminate $ y$ and all positive integers $ m$ if and only if the Hilbert series of $ M$ is in $ \mathcal{H}$. Given two finite graded $ R$-modules $ M$ and $ N$ with the strong Lefschetz property, we determine sufficient conditions in order that $ M\otimes_kN$ has the strong Lefschetz property.


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Additional Information

Melissa Lindsey
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-2067
Email: lindsey9@math.purdue.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10498-7
PII: S 0002-9939(2010)10498-7
Keywords: Hilbert series, strong Lefschetz property
Received by editor(s): September 11, 2009
Received by editor(s) in revised form: March 11, 2010
Published electronically: July 1, 2010
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.