The strong Lefschetz property and simple extensions

Abstract

Stanley showed that monomial complete intersections have the strong Lefschetz property. Extending this result we show that a simple extension of an Artinian Gorenstein algebra with the strong Lefschetz property has again the strong Lefschetz property.

References in corpus (1)

• The Weak and Strong Lefschetz Properties for Artinian K-Algebras

Cited by in corpus (9)

• A tour of the Weak and Strong Lefschetz Properties
• Generic initial ideal for complete intersections of embedding dimension three with strong Lefschetz property
• Conditions for Generic Initial Ideals to be Almost Reverse Lexicographic
• A note on the generic initial ideal for complete intersections
• Generic initial ideals, graded Betti numbers and $k$-Lefschetz properties
• Almost reverse lexicographic ideals and Fröberg sequence
• Generic Initial Ideals of Artinian Ideals Having Lefschetz Properties or The Strong Stanley Property
• Contribution in combinatorics in commutative algebra.(ph-d thesis)
• A Class of Hilbert Series and the Strong Lefschetz Property