Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5773353 | Linear Algebra and its Applications | 2017 | 14 Pages |
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 bSâyS and SbâSx, 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 aRâbR=(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 xâ¤ây' and prove the conjecture when S is an associative ring.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Ravindra B. Bapat, Surender Kumar Jain, K. Manjunatha Prasad Karantha, M. David Raj,