Moufang loops with limited commutativity and one commutator
type: Item
instance of: scholarly article
title: Moufang loops with limited commutativity and one commutator
zbMATH Open document ID: 0628.20054
DOI: 10.1007/BF01194160
author: Orin Chein
author: Edgar G. Goodaire
published in: Archiv der Mathematik
publication date: 1988-01-01T00:00:00Z
review text: A Moufang loop has the limited commutativity property if whenever two elements x and y commute, one of x, y, xy is central. This paper represents the culmination of previous work of the authors dealing with the structure of Moufang loops whose loop rings, over an associative ring of characteristic \(\neq 2\), are alternative rings. [See \textit{E. G. Goodaire}, Publ. Math. 30, 31-38 (1983; Zbl 0537.17006)], and \textit{O. Chein} and \textit{E. G. Goodaire}, Commun. Algebra 14, 293-310 (1986; Zbl 0582.17015).] The main theorem lists six conditions equivalent to the property that a loop L should have an alternative loop ring over some ring of characteristic \(\neq 2\). One of the more curious of these is that L should be a Moufang loop with the limited commutativity property and a unique nonidentity commutator.
Mathematics Subject Classification ID: 20N05
Mathematics Subject Classification ID: 17D05
zbMATH DE Number: 4021466
zbMATH Keywords: limited commutativity
zbMATH Keywords: Moufang loops
zbMATH Keywords: loop rings
zbMATH Keywords: alternative rings
zbMATH Keywords: alternative loop ring
zbMATH Keywords: commutator
MaRDI profile type: Publication
cites work: Q3248988
cites work: Moufang Loops of Small Order. I
cites work: Loops whose loop rings are alternative
cites work: Q3322274
full work available at URL: https://doi.org/10.1007/bf01194160
OpenAlex ID: W2088179711
description: scientific article; zbMATH DE number 4021466