Properties of eventually inverse semigroups. (Q874863)

A semigroup \(S\) is called eventually inverse if for every element \(a\in S\) there exists a positive integer \(m\) such that \(a^m\) is regular and every regular element of \(S\) possesses a unique inverse. Some properties of eventually inverse semigroups and their subsemigroups are studied. An epigroup with a unique idempotent is called a \(\pi\)-group. The minimum \(\pi\)-group congruence on an eventually inverse semigroup is described.