Journal of Commutative Algebra

The strong Lefschetz property in codimension two

David Cook, II

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Abstract

Every artinian quotient of $K[x,y]$ has the strong Lefschetz property if $K$ is a field of characteristic zero or is an infinite field whose characteristic is greater than the regularity of the quotient. We improve this bound in the case of monomial ideals. Using this we classify when both bounds are sharp. Moreover, we prove that the artinian quotient of a monomial ideal in $K[x,y]$ always has the strong Lefschetz property, regardless of the characteristic of the field, exactly when the ideal is lexsegment. As a consequence, we describe a family of non-monomial complete intersections that always have the strong Lefschetz property.

Article information

Source
J. Commut. Algebra, Volume 6, Number 3 (2014), 323-344.

Dates
First available in Project Euclid: 17 November 2014

Permanent link to this document
https://projecteuclid.org/euclid.jca/1416233321

Digital Object Identifier
doi:10.1216/JCA-2014-6-3-323

Mathematical Reviews number (MathSciNet)
MR3278807

Zentralblatt MATH identifier
1303.13019

Subjects
Primary: 13A35: Characteristic p methods (Frobenius endomorphism) and reduction to characteristic p; tight closure [See also 13B22] 13E10: Artinian rings and modules, finite-dimensional algebras

Keywords
Strong Lefschetz property positive characteristic lexsegment ideals

Citation

Cook, David. The strong Lefschetz property in codimension two. J. Commut. Algebra 6 (2014), no. 3, 323--344. doi:10.1216/JCA-2014-6-3-323. https://projecteuclid.org/euclid.jca/1416233321


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