[U.Sup.*]-Inverse Semigroups (1) (Report‪)‬

Abstract The minimum cancellative monoid congruence on [L.sup.*]-inverse semigroups is given in this paper. On the basis, we investigate a subclass of [L.sup.*]-inverse semigroups, namely, [U.sup.*]-inverse semigroups. It is proved that a semigroup S is an [U.sup.*]-inverse semigroup if and only if for any x [member of] S there exist a unique element [x.sup.o] [member of] [H.sub.1]* such that x [less than or equal to] [x.sup.o]. Keywords L*-inverse semigroups, [U.sup.*]-inverse semigroups, cancellative monoids.