Regular matrices and their strong preservers over semirings
type: Item
instance of: scholarly article
title: Regular matrices and their strong preservers over semirings
zbMATH Open document ID: 1152.15004
author: Seok-Zun Song
author: Kyung-Tae Kang
author: Leroy B. Beasley
author: Nung-Sing Sze
published in: Linear Algebra and its Applications
publication date: 2008-06-09T00:00:00Z
review text: Regular elements in a ring as generalized inverse elements were originated by E. H. Moore in 1935. Let \(R\) be a ring. An element \(a\) in this ring is called regular if there is an element \(x\in R\) such that \(axa=a\). When \(x\) exists, it is called a generalized inverse of \(a\). This concept has been considered and studied in rings of matrices. Some authors characterized regular matrices over semirings (R. B. Bapat, J. Denes, K. H. Kim,\dots). The authors of the paper under review consider characterization of linear operators, \(T\) say, on the matrices over semirings, that preserve regularity, i.e. those linear operators, \(T\) for which a matrix \(A\) over a semiring is regular if and only if \(T(A)\) is regular. Their results include the Boolean algebra, the nonnegative reals, the nonnegative integers and the fuzzy scalars.
reviewed by: Manouchehr Misaghian
Mathematics Subject Classification ID: 15A04
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 16Y60
zbMATH DE Number: 5285770
zbMATH Keywords: semiring
zbMATH Keywords: generalized inverse of a matrix
zbMATH Keywords: linear operator
zbMATH Keywords: regular matrix
zbMATH Keywords: linear preservers
Wikidata QID: Q57702661
MaRDI profile type: Publication
full work available at URL: j.laa.2008.02.015
OpenAlex ID: W2070116352
cites work: Structure of a nonnegative regular matrix and its generalized inverses
cites work: Boolean-rank-preserving operators and Boolean-rank-1 spaces
cites work: Q5603210
cites work: Q3758977
cites work: Q3958592
cites work: A Note on Boolean Matrix Theory
cites work: Generalized Inverses of Boolean Relation Matrices
cites work: On generalized inverses of Boolean matrices
cites work: Inverses of Boolean matrices
cites work: LINEAR PRESERVERS OF BOOLEAN NILPOTENT MATRICES
DOI: 10.1016/J.LAA.2008.02.015
description: scientific article; zbMATH DE number 5285770