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Proceedings of the American Mathematical Society

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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
DOI: https://doi.org/10.1090/S0002-9939-2010-10498-7
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

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.