Generalized invertibility in two semigroups of a ring.
type: Item
instance of: scholarly article
title: Generalized invertibility in two semigroups of a ring.
zbMATH Open document ID: 1046.15004
author: P. Patrício
author: R. Puystjens
published in: Linear Algebra and its Applications
publication date: 2004-01-14T00:00:00Z
full work available at URL: http://hdl.handle.net/1822/2888
review text: Let \(R\) be ring with unity and \(e\in R\) be an idempotent. In analogy to matrix rings the notions of Neumann, group, Drazin and Moore-Penrose inverses in \(R\) are defined. The authors prove some general results connecting the above notions and next they apply them to the matrices over a given ring \(R\).
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15A30
Mathematics Subject Classification ID: 16S50
zbMATH DE Number: 2026891
zbMATH Keywords: generalized invertibility
zbMATH Keywords: corner rings
zbMATH Keywords: matrices over rings
zbMATH Keywords: semigroups
zbMATH Keywords: matrix rings
zbMATH Keywords: Moore-Penrose inverses
zbMATH Keywords: generalized inverse matrix
zbMATH Keywords: Neumann inverse
zbMATH Keywords: group inverse
reviewed by: Witold Więsław
MaRDI profile type: Publication
OpenAlex ID: W2168804366
cites work: Q3207128
cites work: Additive results for the generalized Drazin inverse
cites work: Q3922081
cites work: Q4149846
cites work: Q3884160
cites work: Some additive results on Drazin inverse
cites work: The moore-penrose inverse of a matrix over a semi-simpie artinian ring
cites work: Composition of binary quadratic forms
cites work: The Moore-Penrose inverse of von Neumann regular matrices over a ring
cites work: The Moore-Penrose inverse of a factorization
cites work: Generalized inverses of matrices with entries taken from an arbitrary field
cites work: The Moore-Penrose inverse of a morphism with factorization
cites work: Symmetric morphisms and the existence of Moore-Penrose inverses
cites work: Drazin invertibility for matrices over an arbitrary ring
cites work: The group inverse of a companion matrix
DOI: 10.1016/J.LAA.2003.08.004
Recommended article: A new class of generalized inverses in semigroups and rings with involution
Recommended article: Q3774074
Recommended article: INVERSE SEMIGROUPS AND SEMINEAR-RINGS
Recommended article: Generalized inverses modulo ℋ in semigroups and rings
Recommended article: Two generalisations of the symmetric inverse semigroups
Recommended article: Q4624599
Recommended article: Generalized inverses of centralizers of semiprime rings.
Recommended article: Several characterizations for generalized inverses in a ring
Recommended article: On rings with inverse adjoint semigroups
Recommended article: The structure of generalized inverse semigroups.
description: scientific article; zbMATH DE number 2026891