Factoring out the socle of a Gorenstein ring

DOI10.1016/0021-8693(78)90191-6zbMath0407.13018OpenAlexW2081462757MaRDI QIDQ1257932

Luchezar L. Avramov, Gerson Levin

Publication date: 1978

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

Full work available at URL: https://doi.org/10.1016/0021-8693(78)90191-6

zbMATH Keywords

Koszul ComplexPoincare SeriesKoszul HomologyLocal Zero-Dimensional Gorenstein

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)

Related Items (22)

Stable cohomology over local rings ⋮ Connected sums of Gorenstein local rings ⋮ On the rationality of Poincaré series of Gorenstein algebras via Macaulay's correspondence ⋮ The Golod property of powers of the maximal ideal of a local ring ⋮ Local Artinian rings and the Fröberg relation ⋮ Three-dimensional manifolds, skew-Gorenstein rings and their cohomology. ⋮ DETECTING KOSZULNESS AND RELATED HOMOLOGICAL PROPERTIES FROM THE ALGEBRA STRUCTURE OF KOSZUL HOMOLOGY ⋮ Homological criteria for minimal multiplicity ⋮ Poincaré series of modules over compressed Gorenstein local rings ⋮ A Gorenstein numerical semi-group ring having a transcendental series of Betti numbers ⋮ Associated graded rings and connected sums ⋮ Decomposing Gorenstein rings as connected sums ⋮ 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 ⋮ Some criteria for detecting large homomorphisms of local rings ⋮ Subadditivity of syzygies of Koszul algebras ⋮ A family of local rings with rational Poincaré series ⋮ A criterion for modules over Gorenstein local rings to have rational Poincaré series ⋮ Poincaré Series and Deformations of Gorenstein Local Algebras ⋮ A survey on the Koszul homology algebra ⋮ The Poincaré series of a local Gorenstein ring of multiplicity up to 10 is rational ⋮ Commutative rings, algebraic topology, graded Lie algebras and the work of Jan-Erik Roos ⋮ The Poincaré series of a codimension four Gorenstein ring is rational

Cites Work

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• Local rings and Golod homomorphisms
• Rings which are a factor of a Gorenstein ring by its socle
• Homology algebra of the Koszul complex of a local Gorenstein ring
• Massey operations and the Poincaré series of certain local rings

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