The Ext-algebra of a Golod ring
type: Item
instance of: scholarly article
title: The Ext-algebra of a Golod ring
zbMATH Open document ID: 0577.13007
DOI: 10.1016/0022-4049(85)90021-0
author: Gunnar Sjödin
published in: Journal of Pure and Applied Algebra
publication date: 1985-01-01T00:00:00Z
review text: From the editor's note: ''This article was written 9 years ago but, regretfully, appeared only as two preprints (1976-3 and 1976-6 from Univ. Stockh.). The presentation is direct and selfcontained. The proofs highly depend on computation in the Ext-algebra. There are other, perhaps more elegant, proofs today, but this paper gives a good insight in the theory of Golod rings.'' From the introduction: ''We show that it - the Ext-algebra of a Golod ring R - is even finitely presented, and, if \(R=S/\Omega\), where (S,\({\mathfrak p})\) is regular and \({\mathfrak p}^{2r-3}\subset \Omega \subset {\mathfrak p}^ r\) for some \(r\geq 3\), then the relations can be fairly well understood. In the special case \(R=S/{\mathfrak p}^ r\), where (S,\({\mathfrak p})\) is regular, we calculate the Ext-algebra exactly and present the result in terms of Lie algebras. In this case the Ext-algebra is generated by its 1- and 2-dimensional elements.'' Contents: Introduction; Notations and conventions; 1. The minimal resolutions of k for a Golod rings; 2. Examples of Golod rings; 2. The Ext-algebra of a Golod ring; 4. The Ext-algebra of \(R=S/{\mathfrak p}^ r\); 5. The \(Y_ j's\) are in the Lie algebra underlying \(Ext_ R(k,k)\); 6. Special Golod rings; 7. The Ext-algebra of \(R=S/{\mathfrak p}^ r\) (continued).
Mathematics Subject Classification ID: 13D03
Mathematics Subject Classification ID: 13H05
Mathematics Subject Classification ID: 18G15
Mathematics Subject Classification ID: 13D99
zbMATH DE Number: 3922812
zbMATH Keywords: regular local ring
zbMATH Keywords: Ext-algebra
zbMATH Keywords: Golod rings
zbMATH Keywords: Lie algebra
MaRDI profile type: Publication
full work available at URL: 0022-4049(85)90021-0
OpenAlex ID: W2043324200
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cites work: The cohomology structure of certain fibre spaces. I
cites work: Q3265726
cites work: The Poincaré series of a local ring
cites work: Hopf algebras and derivations
cites work: Homology of Noetherian rings and local rings
description: scientific article; zbMATH DE number 3922812