Compressed Algebras: Artin Algebras Having Given Socle Degrees and Maximal Length

DOI10.2307/1999485zbMath0548.13009OpenAlexW4248352144MaRDI QIDQ3340967

Anthony A. Iarrobino

Publication date: 1984

Full work available at URL: https://doi.org/10.2307/1999485

zbMATH Keywords

Hilbert functionregular local ringcompressed algebraspower-sum algebrassocle type of an Artin algebra

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Commutative Artinian rings and modules, finite-dimensional algebras (13E10) Regular local rings (13H05)

Related Items (84)

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Quotients of level algebras of arbitrary type ⋮ Thin algebras of embedding dimension three

Cites Work

• Unnamed Item
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• Unnamed Item
• Über die freien Auflösungen extremaler Cohen-Macaulay-Ringe
• Relations between the type of a point on an algebraic variety and the type of its tangent cone
• Generic finite schemes and Hochschild cocycles
• The number of generators of a colength N ideal in a power series ring
• Schur functors and Schur complexes
• Simplicity of a vector space of forms: Finiteness of the number of complete Hilbert functions
• Eine Bedingung für die Flachheit und das Hilbertpolynom eines graduierten Ringes
• Description de Hilb sup(n) C{X,Y}
• Complete intersections and Gorenstein ideals
• Hilbert functions of graded algebras
• Deformation of schemes defined by vanishing of Pfaffians
• Reducibility of the families of O-dimensional schemes on a variety
• On the deviation and the type of a Cohen-Macaulay ring
• Géométrie des schémas de Hilbert ponctuels
• THE LINEAR SYZYGIES OF GENERIC FORMS
• Pathologies IV
• Punctual Hilbert schemes
• Algebra Structures for Finite Free Resolutions, and Some Structure Theorems for Ideals of Codimension 3
• Géométrie des points épais
• Stretched Gorenstein Rings

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