On the cohomology of one-relator associative algebras
type: Item
instance of: scholarly article
title: On the cohomology of one-relator associative algebras
zbMATH Open document ID: 0588.16014
DOI: 10.1016/0021-8693(85)90075-4
author: Warren Dicks
published in: Journal of Algebra
publication date: 1985-01-01T00:00:00Z
review text: Let F be a free (associative) algebra over a field k and \(a\in F\setminus k\). If A is the (two-sided) principal ideal generated by a, then \(R=F/A\) is naturally called one-relator algebra. Unlike the commutative setting even nontriviality of R (meaning that \(0\neq 1\) in R) is a difficult question which is still not answered in general. So one-relator algebras are very interesting objects and the author is one of the leaders in their study. In this paper he gives a lot of simplified proofs of various authors and obtains new results, which are concerned primarily with the homological characterization of R. (There is a misprint on page 86, line 11 from the bottom, where B should be replaced by \({\mathfrak b}.)\)
Mathematics Subject Classification ID: 16P10
Mathematics Subject Classification ID: 16S10
Mathematics Subject Classification ID: 16Exx
Mathematics Subject Classification ID: 16E40
zbMATH DE Number: 3944065
zbMATH Keywords: free algebra
zbMATH Keywords: one-relator algebras
zbMATH Keywords: homological characterization
reviewed by: Leonid Makar-Limanov
MaRDI profile type: Publication
full work available at URL: 0021-8693(85)90075-4
OpenAlex ID: W2028435246
cites work: Q4177724
cites work: On universal derivations
cites work: Universal derivations and universal ring constructions
cites work: Q5639812
cites work: Homogeneous elements of free algebras have free idealizers
cites work: A Free Algebra can Be Free as a Module over a Nonfree Subalgebra
cites work: Distributive lattices of subspaces and the equality problem for algebras with a single relation
cites work: On a Theorem of Cohen and Lyndon About Free Bases for Normal Subgroups
cites work: Algèbres de Lie et pro-p-groupes définis par une seule relation
cites work: Q5682494
cites work: A Matrix Representation for Associative Algebras. I
cites work: Cohomology theory of groups with a single defining relation
cites work: Algebraically closed skew fields
description: scientific article; zbMATH DE number 3944065