Reverse order laws in rings with involution.
type: Item
instance of: scholarly article
title: Reverse order laws in rings with involution.
zbMATH Open document ID: 1321.16025
DOI: 10.1216/RMJ-2014-44-4-1301
author: Dijana Mosić
author: Dragan S. Djordjević
published in: Rocky Mountain Journal of Mathematics
publication date: 2014-11-12T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.rmjm/1414760955
review text: In a ring with involution, \(a^\#\) stands for the group inverse, and \(a^\dagger\) for the Moore-Penrose inverse of \(a\). Various equivalent conditions to each of a number reverse order laws are presented. Among these laws are \((ab)^\#=b^\#(a^\dagger abb^\#)^\#a^\dagger\), \((ab)^\#=b^*(a^\#abb^*)^\#a^\#\), \((ab)^\#=b^\dagger a^\#\), \(b^\#(a^*abb^\#)^\#a^*=b^\#a^*\), \((abb^\dagger)^\#=(a^\#abb^\dagger)^\#a^\#\), and their variants. Also, sufficient conditions for each of several laws (similar to the first two above) are found.
reviewed by: Jānis Cīrulis
Mathematics Subject Classification ID: 16W10
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 46L05
zbMATH DE Number: 6368767
zbMATH Keywords: group inverses
zbMATH Keywords: Moore-Penrose inverses
zbMATH Keywords: reverse order laws
zbMATH Keywords: rings with involution
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6368767