Left absolutely flat generalized inverse semigroups

A semigroup S is called (left, right) absolutely flat if all of its (left, right) S-sets are flat. S is a (left, right) generalized inverse semigroup if S is regula, and its set of idempotents 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 is left absolutely flat if and only if S is a right generalized inverse semigroup and the (nonidentity) structure maps of E(S) are constant. In particular all inverse semigroups are left (and right) absolutely flat (see (1)). Other consequences are derived.