Poincaré series of short Artinian rings

DOI10.1016/0021-8693(85)90023-7zbMath0572.13001OpenAlexW2018599712MaRDI QIDQ1062100

Jörgen Backelin, Ralf Fröberg

Publication date: 1985

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

Full work available at URL: https://doi.org/10.1016/0021-8693(85)90023-7

zbMATH Keywords

Hilbert seriesgraded Artinian ringsrationality of Poincaré seriesgraded Cohen-Macaulay rings

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Multiplicity theory and related topics (13H15) (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.) (13D03) Commutative Artinian rings and modules, finite-dimensional algebras (13E10)

Related Items (9)

On the Cohen-Macaulay property for quadratic tangent cones ⋮ Poincaré series of modules over local rings of small embedding codepth or small linking number ⋮ Local Artinian rings and the Fröberg relation ⋮ The Koszul property for spaces of quadrics of codimension three ⋮ A computer-aided study of the graded Lie algebra of a local commutative noetherian ring. -- Appendix A: Some technical details about how the computer was used. -- Appendix B (by Clas Löfwall): The Lie algebra structure of a ring satisfying \({\mathcal M}_ 3\) and variants ⋮ Gröbner bases for spaces of quadrics of codimension 3 ⋮ On computer-assisted research in homological algebra. ⋮ Good and bad Koszul algebras and their Hochschild homology ⋮ Generalized hilbert numerators

Cites Work

• A counterexample to a conjecture of Serre
• Small homomorphisms of local rings
• The Poincaré series of a local ring
• Determination of a class of Poincaré series.
• Nets of conics

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