Characterizations and representations of outer inverse for matrices over a ring. Issue 1 (2nd January 2021)

• Record Type: Journal Article
• Authors: Ke, Yuanyuan; Chen, Jianlong; Stanimirović, Predrag; Ćirić, Miroslav
• Is Part Of: Linear & multilinear algebra. Volume 69:Issue 1(2021)
• Page Start: 155
• Page End: 176
• Publication Date: 2021-01-02
• Subjects: Generalized inverse -- AT, S(2) -- (b, c)-inverse -- the inverse along an element -- semigroup; 15A09 -- 16E50 -- 16B99; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2019.1590302
• Languages: English
• ISSNs: 0308-1087

Abstract

Abstract : In this paper, we investigate the existence and representations of the generalized inverse A T, ∗ ( 2 ), A T, ∗ ( 1, 2 ), A ∗, S ( 2 ), A ∗, S ( 1, 2 ), A T, S ( 2 ), A T, S ( 1, 2 ) of a matrix A over an associative ring, and give some characterizations and representations of these generalized inverses by using regularity. Some explicit expressions for A T, S ( 2 ) and A T, S ( 1, 2 ) of a matrix A by means of { 1 } -inverse are also given. Furthermore, we present the relationship between the generalized inverse A T, S ( 2 ) and the ( B, C ) -inverse of a matrix A over rings. And then using the regularity give the sufficient and necessary condition for the existence and the expression of ( B, C ) -inverse of matrices over a ring. Some explicit expressions for ( b, c ) -inverse of an element in semigroups by means of { 1 } -inverse are also studied. As applications, some new results for the Mary inverse, the core inverse and dual core inverse are obtained.