On the homology of commutative algebras
type: Item
instance of: scholarly article
title: On the homology of commutative algebras
zbMATH Open document ID: 0769.13008
DOI: 10.1016/0022-4049(92)90154-8
author: J. L. Doncel
author: M. J. Vale
author: A. R. Grandjeán
published in: Journal of Pure and Applied Algebra
publication date: 1993-01-16T00:00:00Z
review text: The authors give a method for computing the homology and cohomology groups of a commutative \(A\)-algebra \(B\) with coefficients in a \(B\)-module \(M\). It is extended the 2-fold crossed module of the theory of groups to commutative algebra, and using 2-crossed resolutions and the homotopy operator, it is defined a homology theory and it is proved that it coincides with the André-Quillen theory for \(n=0,1,2,3\). Using this linear method it is obtained the Jacobi-Zariski sequence. The authors use these results to characterize complete intersection rings by the vanishing of the third homology group. The corresponding results for cohomology also hold.
Mathematics Subject Classification ID: 13D03
Mathematics Subject Classification ID: 13C40
zbMATH DE Number: 89566
zbMATH Keywords: homology
zbMATH Keywords: cohomology
zbMATH Keywords: 2-fold crossed module
zbMATH Keywords: André-Quillen theory
zbMATH Keywords: Jacobi-Zariski sequence
zbMATH Keywords: complete intersection rings
reviewed by: Iuliu Crivei
MaRDI profile type: Publication
full work available at URL: 0022-4049(92)90154-8
OpenAlex ID: W1969160367
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description: scientific article; zbMATH DE number 89566