Maximal Dense Ideal Extensions of Locally Inverse Semigroups

Almost Factorizable Locally Inverse Semigroups

“…We use the main idea of the proof of [15,Lemma 3.11]. Let H, H ∈ U with H ∈ V (H) and let a ∈ H. Since HH H = H, there exist elements a 1 , a 2 ∈ H and a † ∈ H such that a = a 1 a † a 2 , and, applying the same idea for a 1 , there exist…”

“…The aim of this paper is to introduce a notion of an almost factorizable locally inverse semigroup so that these semigroups turn out to form a natural class containing all Pastijn products of normal bands by completely simple semigroups and being closed under forming homomorphic images. Recently, Pastijn and Oliveira [15] have provided an analog of the monoid of permissible subsets of an inverse semigroup for any locally inverse semigroup. However, this does not lead to a notion of almost factorizability we are seeking for.…”