On semialternative algebras
type: Item
instance of: scholarly article
title: On semialternative algebras
zbMATH Open document ID: 0785.17002
DOI: 10.1016/0021-8693(92)90100-Z
published in: Journal of Algebra
publication date: 1993-03-29T00:00:00Z
review text: A nonassociative ring satisfying the identity \((x,y,z)= (y,z,x)\) is called semialternative. The authors assume finite dimensionality and characteristic \(\neq 2,3\). They define the radical as the maximal solvable ideal and show that this radical is nilpotent. If the ring has an idempotent, they find its Peirce decomposition and subspace multiplication table. They have an example which shows that the Wedderburn principal theorem does not hold. Over a field of characteristic 0, they define a trace form \((x,y):=\) the trace of right multiplication by \(xy\). Then \((xy,z)=(x,yz)\) and the radical of the bilinear form is the same as the radical previously defined.
Mathematics Subject Classification ID: 17A30
Mathematics Subject Classification ID: 17A65
zbMATH DE Number: 130497
zbMATH Keywords: associator
zbMATH Keywords: semialternative ring
zbMATH Keywords: radical
zbMATH Keywords: Peirce decomposition
zbMATH Keywords: trace form
author: Schafer, R. D.
reviewed by: Irvin Roy Hentzel
MaRDI profile type: Publication
cites work: Assosymmetric Rings
cites work: Rings satisfying (x,y,z) = (y,z,x)
cites work: An Extension of the Class of Alternative Rings
cites work: Q5522244
cites work: Rings Satisfying (x, y, z) = (y, z, x)
description: scientific article; zbMATH DE number 130497