Level Algebras, Lex Segments, and Minimal Hilbert Functions

DOI10.1081/AGB-120017774zbMath1094.13520OpenAlexW2001052549MaRDI QIDQ4802446

Anna Maria Bigatti, Anthony V. Geramita

Publication date: 14 April 2003

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

Full work available at URL: https://doi.org/10.1081/agb-120017774

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Syzygies, resolutions, complexes and commutative rings (13D02) Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics (13A30) Commutative Artinian rings and modules, finite-dimensional algebras (13E10)

Related Items

On the Resolution of Certain Level Algebras, Extending the idea of compressed algebra to arbitrary socle-vectors. II: Cases of non-existence, On Gorenstein sequences of socle degrees 4 and 5, Interval conjectures for level Hilbert functions, The strength of the weak Lefschetz property, Betti numbers of polynomial hierarchical models for experimental designs, The Hilbert functions which force the Weak Lefschetz property, Generic initial ideals and graded Artinian-level algebras not having the weak-Lefschetz property, On parameter spaces for Artin level algebras., On the degree two entry of a Gorenstein $h$-vector and a conjecture of Stanley, Extending the idea of compressed algebra to arbitrary socle-vectors., Ancestor ideals of vector spaces of forms, and level algebras., Artinian level algebras of codimension 3, Unnamed Item, On the shape of a pure 𝑂-sequence, Nonunimodal Gorenstein sequences of higher socle degrees, Artinian Level Algebras of Low Socle Degree, Some algebraic consequences of Green's hyperplane restriction theorems, Hilbert functions and level algebras, CANCELLATION IN RESOLUTIONS AND LEVEL ALGEBRAS, Reducible family of height three level algebras, Forcing the strong Lefschetz and the maximal rank properties, Bounds and asymptotic minimal growth for Gorenstein Hilbert functions, Level Algebras of Type 2, When Is There a Unique Socle-Vector Associated to a Givenh-Vector?, Almost maximal growth of the Hilbert function

Cites Work

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• Upper bounds for the betti numbers of a given hilbert function
• Maximum betti numbers of homogeneous ideals with a given hilbert function
• Hilbert functions and level algebras