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Normal Subloops in the Integral Loop Ring of an RA Loop

Published online by Cambridge University Press:  20 November 2018

Edgar G. Goodaire  and
César Polcino Milies
Edgar G. Goodaire
Affiliation:
Memorial University of Newfoundland St. John’s, Newfoundland A1C 5S7, email: edgar@math.mun.ca
César Polcino Milies
Affiliation:
Instituto de Matemática e Estatística Universidade de São Paulo Caixa Postal 66.281 CEP 05315-970 São Paulo SP Brasil, email: polcino@ime.usp.br
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Abstract

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We show that an $\text{RA}$ loop has a torsion-free normal complement in the loop of normalized units of its integral loop ring. We also investigate whether an $\text{RA}$ loop can be normal in its unit loop. Over fields, this can never happen.

Keywords

20N0517D0516S3416U60
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 44 , Issue 1 , 01 March 2001 , pp. 27 - 35
Copyright
Copyright © Canadian Mathematical Society 2001

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