Outer inverses: Characterization and applications

Ravindra B. Bapat, Surender Kumar Jain, K. Manjunatha Prasad Karantha, M. David Raj

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)171-184
Number of pages14
JournalLinear Algebra and Its Applications
Publication statusPublished - 01-09-2017

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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