Invertible linear maps preserving \(\{1\}\)-inverses of matrices over PID
type: Item
instance of: scholarly article
title: Invertible linear maps preserving \(\{1\}\)-inverses of matrices over PID
zbMATH Open document ID: 1121.15002
DOI: 10.1007/BF02832051
author: Changjiang Bu
published in: Journal of Applied Mathematics and Computing
publication date: 2007-01-29T00:00:00Z
review text: Let \(R\) be a principal ideal domain of characteristic two. The author classifies linear bijections \(f:M_n(R)\to M_n(R)\) with the property that \(AXA=A\) implies \(f(A)f(X)f(A)=f(A)\). The proof first shows that \(f\) is unital, and then uses the fact that, in characteristic two, \(B^2=B\) is equivalent to \(B^3=B\) and \((B+I)^3=(B+I)\). Consequently, \(f\) preserves idempotents.
reviewed by: Bojan Kuzma
Mathematics Subject Classification ID: 15A04
Mathematics Subject Classification ID: 15A09
zbMATH DE Number: 5119547
zbMATH Keywords: principal ideal domain
zbMATH Keywords: {1}-inverse of a matrix
zbMATH Keywords: linear preserver, Jordan triple product
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5119547