Left absolutely flat generalized inverse semigroups

Abstract

A semigroup S S is called (left, right) absolutely flat if all of its (left, right) S S -sets are flat. S S is a (left, right) generalized inverse semigroup if S S is regular and its set of idempotents E ( S ) E(S) is a (left, right) normal band (i.e. a strong semilattice of (left zero, right zero) rectangular bands). In this paper it is proved that a generalized inverse semigroup S S is left absolutely flat if and only if S S is a right generalized inverse semigroup and the (nonidentity) structure maps of E ( S ) E(S) are constant. In particular all inverse semigroups are left (and right) absolutely flat (see [1]). Other consequences are derived.