On a problem of commutativity of automorphisms
type: Item
instance of: scholarly article
title: On a problem of commutativity of automorphisms
zbMATH Open document ID: 0897.16019
DOI: 10.1155/S016117129800057X
author: A. B. Thaheem
author: Muhammad Anwar Chaudhry
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1998-10-12T00:00:00Z
full work available at URL: https://eudml.org/doc/47983
review text: Summary: We provide a partial answer to a problem proposed by M. Brešar. We prove that if \(\alpha\), \(\beta\) are automorphisms of a commutative prime ring of characteristic not equal to 2 satisfying the equation \(\alpha+\alpha^{-1}=\beta+\beta^{-1}\), then either \(\alpha=\beta\) or \(\alpha=\beta^{-1}\). As a consequence \(\alpha\) and \(\beta\) commute and in this situation the equation itself ensures the commutativity of \(\alpha\) and \(\beta\).
Mathematics Subject Classification ID: 16W20
Mathematics Subject Classification ID: 46L40
Mathematics Subject Classification ID: 16N60
zbMATH DE Number: 1140288
zbMATH Keywords: automorphisms
zbMATH Keywords: prime rings
zbMATH Keywords: commutativity
MaRDI profile type: Publication
OpenAlex ID: W2045372023
description: scientific article; zbMATH DE number 1140288