Journal of Commutative Algebra

The strong Lefschetz property in codimension two

David Cook, II

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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.

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

First available in Project Euclid: 17 November 2014

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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

Strong Lefschetz property positive characteristic lexsegment ideals


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.

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