A construction of loops which admit right alternative loop rings
type: Item
instance of: scholarly article
title: A construction of loops which admit right alternative loop rings
zbMATH Open document ID: 0861.20058
DOI: 10.1007/BF03322204
author: Edgar G. Goodaire
author: D. A. Robinson
published in: Results in Mathematics
publication date: 1997-05-20T00:00:00Z
review text: It is known [see \textit{O. Chein} and \textit{E. G. Goodaire}, Algebras Groups Geom. 5, No. 3, 297-304 (1989; Zbl 0696.17016)] that -- if a loop ring \(RL\) is right alternative and \(\text{char }R\neq 2\), then \(RL\) is necessarily left alternative, -- if \(L\) is Moufang and if \(RL\) is right alternative (regardless of the characteristic of \(R\)), then \(RL\) must be left alternative. Thus if \(RL\) is a right, but not left, alternative ring, then \(\text{char }R\) must be 2 and \(L\) cannot be Moufang. Theorem 3.1. of this paper gives a specific construction of loops whose loop rings are right, but not left, alternative.
Mathematics Subject Classification ID: 20N05
Mathematics Subject Classification ID: 17D15
Mathematics Subject Classification ID: 17D05
zbMATH DE Number: 872698
zbMATH Keywords: right alternative rings
zbMATH Keywords: loop rings
reviewed by: Elena Broží ková
MaRDI profile type: Publication
cites work: Q3248988
cites work: Q3472277
cites work: A class of loops with right alternative loop rings
cites work: On \(K\)-loops of finite order
cites work: Bol Loops
full work available at URL: https://doi.org/10.1007/bf03322204
OpenAlex ID: W1970192838
description: scientific article; zbMATH DE number 872698