Almost factorizable weakly type B semigroups

The definition of an almost left factorizable weakly type B semigroup is introduced by using the notion of a left factorizable weakly type B monoids, and some properties and characterizations on such semigroup are obtained. The main aim of this paper is to give characterizations of sufficient and necessary conditions for a weakly type B semigroup to be almost left factorizable. In particular, some properties of proper almost factorizable weakly type B semigroups are given.