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Regular version of the site

Article

A counterexample on outer inverses in semigroups

Linear Algebra and its Applications. 2017. Vol. 513. P. 120-121.
Shitov Y.

We construct a counterexample to the following conjecture, which was proposed recently by Bapat et al. ‘If a is a regular element in a semigroup S, and x is an outer inverse of a, then a has a reflexive generalized inverse y which dominates x with respect to the minus order on S.’