Abstract. We introduce the notion of a factorisable and an almost factorisable straight locally inverse semigroup, and prove that every straight locally inverse semigroup can be obtained as a subsemigroup of an idempotent separating homomorphic image of a Pastijn product of a semilattice by a completely simple semigroup. Moreover, we give an alternative proof of the fact that each straight locally inverse semigroup has a weakly $E$-unitary cover, implicitely due to Pastijn.

AMS Subject Classification (1991): 20M17, 20M10

Received March 19, 2002, and in revised form November 10, 2002. (Registered under 2917/2009.)