The Poincaré series of a codimension four Gorenstein ring is rational

DOI10.1016/0022-4049(85)90013-1zbMath0575.13007OpenAlexW1999808404MaRDI QIDQ1064355

Andrew R. Kustin, Carl Jacobsson, Matthew P. Miller

Publication date: 1985

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-4049(85)90013-1

zbMATH Keywords

Gorenstein ringregular local ringhomotopy Lie algebrarationality of Poincaré seriesGolod map

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.) (13D03) Abstract and axiomatic homotopy theory in algebraic topology (55U35) Regular local rings (13H05) Homological methods in commutative ring theory (13D99)

Related Items

Linkage theory for algebras with pure resolutions ⋮ The Poincaré series of every finitely generated module over a codimension four almost complete intersection is a rational function ⋮ Growth of Betti numbers of modules over local rings of small embedding codimension or small linkage number ⋮ Vanishing of cohomology over Gorenstein rings of small codimension ⋮ 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 ⋮ The Poincaré series of the module of derivations of affine monomial curves ⋮ Poincaré series of modules over local rings of small embedding codepth or small linking number ⋮ Persistence of homology over commutative Noetherian rings ⋮ Free resolutions over short Gorenstein local rings ⋮ Gorenstein algebras of codimension four and characteristic two ⋮ Classification of the Tor-Algebras of Codimension Four Almost Complete Intersections ⋮ 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 ⋮ Classification of the Tor-algebras of codimension four Gorenstein local rings ⋮ Local rings over which all modules have rational Poincaré series ⋮ On the minimal free resolution of $n+1$ general forms

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Classification of the Tor-algebras of codimension four Gorenstein local rings
• Algebra structures on minimal resolutions of Gorenstein rings of embedding codimension four
• Local rings and Golod homomorphisms
• Small homomorphisms of local rings
• Factoring out the socle of a Gorenstein ring
• Certain complexes associated to a sequence and a matrix
• A proof of the existence of minimal R-algebra resolutions
• Über homologische Invarianten lokaler Ringe
• Massey operations and the Poincaré series of certain local rings
• Free Lie Subalgebras of the Cohomology of Local Rings
• Berechnung einiger Poincaré-Reihen
• On the deviations of a local ring.
• Multiplicative Structure on Resolutions of Algebras Defined by Herzog Ideals
• Two Applications of Change of Rings Theorems for Poincare-Series
• Tate resolutions for commutative graded algebras over a local ring