On left quasinormal orthodox semigroups
Gracinda M. S. Gomes · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1983
Synopsis The existence of a smallest inverse congruence on an orthodox semigroup is known. It is also known that a regular semigroupSis locally inverse and orthodox if and only if there exists a local isomorphism fromSonto an inverse semigroupT. In this paper, we show the existence of a smallestR-unipotent congruence ρ on an orthodox semigroupSand give its expression in the case whereSis also left quasinormal. Finally, we prove that a regular semigroupSis left quasinormal and orthodox if and only if there exists a local isomorphism fromSonto anR-unipotent semigroupT.