Outer inverses: Characterization and applications

Authors

Ravindra B. Bapat, Indian Statistical Institute (Delhi Centre)
Surender Kumar Jain, King Abdulaziz University
K. Manjunatha Prasad Karantha, Manipal Academy of Higher Education
M. David Raj, Manipal Academy of Higher Education

Article Type

Research Article

Publication Title

Linear Algebra and Its Applications

Abstract

We characterize the elements with outer inverse in a semigroup S, and provide explicit expressions for the class of outer inverses b of an element a such that bS⊆yS and Sb⊆Sx, where x, y are any arbitrary elements of S. We apply this result to characterize pairs of outer inverses of given elements from an associative ring R, satisfying absorption laws extended for the outer inverses. We extend the result on right–left symmetry of aR⊕bR=(a+b)R (Jain–Prasad, 1998) to the general case of an associative ring. We conjecture that ‘given an outer inverse x of a regular element a in a semigroup S, there exists a reflexive generalized inverse y of a such that x≤−y' and prove the conjecture when S is an associative ring.

First Page

171

Last Page

184

DOI

10.1016/j.laa.2016.06.045

Publication Date

9-1-2017

Comments

Open Access, Bronze

Recommended Citation

Bapat, Ravindra B.; Jain, Surender Kumar; Karantha, K. Manjunatha Prasad; and Raj, M. David, "Outer inverses: Characterization and applications" (2017). Journal Articles. 2448.
https://digitalcommons.isical.ac.in/journal-articles/2448