Journal of Commutative Algebra
- J. Commut. Algebra
- Volume 6, Number 3 (2014), 323-344.
The strong Lefschetz property in codimension two
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.
J. Commut. Algebra, Volume 6, Number 3 (2014), 323-344.
First available in Project Euclid: 17 November 2014
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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