The strong Lefschetz property for Artinian algebras with non-standard grading

DOI10.1016/j.jalgebra.2007.01.019zbMath1133.13021arXivmath/0702444OpenAlexW1965585123MaRDI QIDQ2370135

Junzo Watanabe, Tadahito Harima

Publication date: 22 June 2007

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0702444

zbMATH Keywords

Hilbert functionGorenstein algebranilpotent matrixstrong Lefschetz propertyArtinian algebra

Mathematics Subject Classification ID

Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Commutative Artinian rings and modules, finite-dimensional algebras (13E10)

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Cites Work

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• The central simple modules of Artinian Gorenstein algebras
• The weak and strong Lefschetz properties for Artinian \(K\)-algebras
• Zero-dimensional Gorenstein algebras with the action of the symmetric group
• The finite free extension of Artinian \(K\)-algebras with the strong Lefschetz property
• Erratum to: ``The finite free extension of Artinian \(K\)-algebras with the strong Lefschetz property
• Lefschetz Property, Schur–Weyl Duality and aq-Deformation of Specht polynomial
• The Lefschetz Property for Componentwise Linear Ideals and Gotzmann Ideals
• A Note on Gorenstein Rings of Embedding Codimension Three