Result: Generalized invertibility in two semigroups of a ring: Generalized invertibility in two semigroups of a ring.

Title:
Generalized invertibility in two semigroups of a ring: Generalized invertibility in two semigroups of a ring.
Authors:
Patrício, Pedro, Puystjens, Roland
Contributors:
Universidade do Minho
Source:
Linear Algebra and its Applications. 377:125-139
Publisher Information:
Elsevier BV, 2004.
Publication Year:
2004
Subject Terms:
Numerical Analysis, Generalized invertibility, Algebra and Number Theory, Algebraic systems of matrices, Corner rings, Moore-Penrose inverses, Matrices over rings, Endomorphism rings, matrix rings, 01 natural sciences, semigroups, group inverse, generalized inverse matrix, Discrete Mathematics and Combinatorics, generalized invertibility, Theory of matrix inversion and generalized inverses, corner rings, Geometry and Topology, 0101 mathematics, Semigroups, matrices over rings, Neumann inverse
Document Type:
Academic journal Article
File Description:
application/xml; application/pdf
Language:
English
ISSN:
0024-3795
DOI:
10.1016/j.laa.2003.08.004
Access URL:
https://zbmath.org/2026891
https://doi.org/10.1016/j.laa.2003.08.004
https://www.sciencedirect.com/science/article/pii/S0024379503007092
https://core.ac.uk/display/82236760
https://repositorium.sdum.uminho.pt/bitstream/1822/2888/1/gismgrp.pdf
https://www.sciencedirect.com/science/article/abs/pii/S0024379503007092
https://repositorium.sdum.uminho.pt/handle/1822/2888
https://hdl.handle.net/1822/2888
Rights:
Elsevier Non-Commercial
Accession Number:
edsair.doi.dedup.....6d062135fb8dcbb7a858f3f759ebd23f
Database:
OpenAIRE

Further Information

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 \(R\).