Factorization of units and groups of stable homotopy equivalences
type: Item
instance of: scholarly article
title: Factorization of units and groups of stable homotopy equivalences
zbMATH Open document ID: 1014.16030
DOI: 10.1016/S0022-4049(01)00171-2
author: Petar Pavešić
published in: Journal of Pure and Applied Algebra
publication date: 2002-08-22T00:00:00Z
review text: Let \(R\) be a ring with 1 and let \(R^*\) denote the group of units in \(R\). A subgroup \(G\) of \(R^*\) is said to be factorizable if \(G=A\cdot B\), where \(A,B\) are subgroups and \(A\cap B=(1)\). The author proves that if \(e\) is an idempotent and \(e+(1-e)G\subset G\) then \(G=(e+(1-e)G)\cdot((1-e)+eG)\) is a factorization. The factorization is a semi-direct product when at least one of the factors is normal in \(G\). The results are applied to computations of groups of stable homotopy equivalences.
Mathematics Subject Classification ID: 16U60
Mathematics Subject Classification ID: 55P42
zbMATH DE Number: 1787475
zbMATH Keywords: groups of units
zbMATH Keywords: factorizable groups
zbMATH Keywords: idempotents
zbMATH Keywords: groups of stable homotopy equivalences
reviewed by: Kwangil Koh
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1787475