Code loops are RA2 loops
type: Item
instance of: scholarly article
title: Code loops are RA2 loops
zbMATH Open document ID: 0695.20041
DOI: 10.1016/0021-8693(90)90088-6
author: Orin Chein
author: Edgar G. Goodaire
published in: Journal of Algebra
publication date: 1990-01-01T00:00:00Z
review text: The authors prove that a nonassociative Moufang loop with a unique nonidentity square must, in fact, have an alternative loop ring over any ring of characteristic two. So, the main result of the paper is the Theorem: If L is a nonassociative Moufang loop with a unique nonidentity square, e, then L is an RA2 loop. An RA2 loop is a nonassociative loop whose loop ring over some ring of characteristic two is alternative.
Mathematics Subject Classification ID: 20N05
Mathematics Subject Classification ID: 17D05
zbMATH DE Number: 4138057
zbMATH Keywords: nonassociative Moufang loop
zbMATH Keywords: alternative loop ring
zbMATH Keywords: RA2 loop
reviewed by: C. Pereira da Silva
MaRDI profile type: Publication
full work available at URL: 0021-8693(90)90088-6
OpenAlex ID: W2085262503
cites work: Q5515384
cites work: Isomorphism of loops which have alternative loop rings
cites work: Loops whose loop rings are alternative
cites work: Moufang loops with limited commutativity and one commutator
cites work: Loops whose loop rings in characteristic 2 are alternative
cites work: Moufang loops with a unique nonidentity commutator (associator, square)
cites work: A simple construction for the Fischer-Griess monster group
cites work: Q3322274
cites work: Code loops
description: scientific article; zbMATH DE number 4138057