The Ext-algebra of a Golod ring
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).
scientific article; zbMATH DE number 3922812
scientific article