Generalized invertibility in a corner ring | Zendy

Long Wang | Zendy; Jianlong Chen | Zendy

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Generalized invertibility in a corner ring

Author(s) -

Long Wang,

Jianlong Chen

Publication year - 2017

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1708189w

Subject(s) - mathematics , drazin inverse , ring (chemistry) , inverse , pure mathematics , involution (esoterism) , product (mathematics) , combinatorics , geometry , law , chemistry , organic chemistry , politics , political science

Let $R$ be a ring with unity and let $a, g\in R$ be such that $a$ is regular. In this article, the generalized invertibility of $ag+1-aa^{-}$ are investigated in term of the generalized invertibility of elements in a corner ring. As applications, several equivalent conditions on the Drazin invertibility of product and difference of idempotents are obtained. Moreover, we present the equivalent conditions for the existence of Moore-Penrose inverse in a ring with involution.

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