Almost Factorizable Locally Inverse Semigroups

Abstract

We introduce a notion of almost factorizability within the class of all locally inverse semigroups by requiring a property of order ideals, and we prove that the almost factorizable locally inverse semigroups are just the homomorphic images of Pastijn products of normal bands by completely simple semigroups.

Structure theory of regular semigroups

“…Homomorphic images of Pastijn products are studied by the author in [62]. A locally inverse semigroup S is called almost factorizable if there exists a completely simple subsemigroup U in the semigroup O(S) of all order ideals of S such that E(U) = E(S) and U ⊇ S. The result obtained is an exact generalization of the characterization of almost factorizable inverse semigroups in terms of semidirect products of semilattices by groups.…”

“…Theorem 5.6 (Szendrei [62]). For any locally inverse semigroup S, the following statements are equivalent:…”