Moufang quasigroups
type: Item
instance of: scholarly article
title: Moufang quasigroups
zbMATH Open document ID: 0855.20056
author: Kenneth Kunen
published in: Journal of Algebra
publication date: 1997-02-02T00:00:00Z
review text: It is well known that the following four Moufang identities, M1: \((x(yz))x=(xy)(zx)\) and N1: \(((xy)z)y=x(y(zy))\) and their respective mirrors M2 and N2 (obtained by writing them backwards), are equivalent in loops which are then called Moufang loops. The author now shows that every quasigroup satisfying any one of these four identities is a Moufang loop, so that in fact these identities are equivalent in quasigroups. The proofs have been aided (not produced) by the automated deduction tool OTTER, developed by W. W. McCune.
Mathematics Subject Classification ID: 20N05
zbMATH DE Number: 923681
zbMATH Keywords: Moufang identities
zbMATH Keywords: Moufang loops
zbMATH Keywords: quasigroups
zbMATH Keywords: automated deduction
zbMATH Keywords: OTTER
Wikidata QID: Q56430424
MaRDI profile type: Publication
full work available at URL: jabr.1996.0216
OpenAlex ID: W4212767513
DOI: 10.1006/JABR.1996.0216
description: scientific article; zbMATH DE number 923681