Jordan decompositions in alternative loop rings
type: Item
instance of: scholarly article
title: Jordan decompositions in alternative loop rings
zbMATH Open document ID: 1009.17021
DOI: 10.1007/BF02843921
author: Ashwani K. Bhandari
author: Anjana Kaila
publication date: 2002-12-17T00:00:00Z
review text: It is well known that, if \(G\) is a finite group and \(K\) a field of characteristic zero, then every element \(\alpha\) of the group ring \(KG\) possesses a decomposition as a sum of commuting semisimple and nilpotent elements, and, if \(\alpha\) is a unit, then this yields an expression for \(\alpha\) as a product of a semisimple and unipotent element. In this paper the question of the existence of such decompositions when the group is replaced by a finite \(RA\) loop \(L\) is considered. One result that can be stated simply is that \(ZL\) has additive Jordan decomposition if and only if \(L\) is a Hamiltonian Moufang RA 2-loop.
reviewed by: Sheila Oates-Williams
Mathematics Subject Classification ID: 17D05
Mathematics Subject Classification ID: 20N05
zbMATH DE Number: 1846830
zbMATH Keywords: alternative rings
zbMATH Keywords: Moufang loops
zbMATH Keywords: Jordan decomposition
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02843921
OpenAlex ID: W2031248428
published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 1846830