Outer inverses: Characterization and applications

Prasad, Manjunatha K and Raj, David M (2017) Outer inverses: Characterization and applications. Linear Algebra and its Applications, 528 (1). pp. 171-184. ISSN 0024-3795

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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.

Item Type: Article
Uncontrolled Keywords: Regular element; generalized inverse; outer inverse; minus partial order; absorption law; associative ring.
Subjects: Departments at MU > Statistics
Depositing User: KMC Library
Date Deposited: 25 May 2017 08:52
Last Modified: 25 May 2017 08:52
URI: http://eprints.manipal.edu/id/eprint/148960

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