Left Orders in Special Completely 0-Simple Semigroups

摘要

A subsemigroup S of a semigroup Q is a left order in Q, and Q is a semigroup of left quotients of S, if every element of Q can be written as a~(-1) b for some a, b ∈ S with a belonging to a group H-class of Q. Characterizations are provided for semigroups which are left orders in completely 0-simple semigroups in the following classes: without similar L-classes, without contractions, R-unipotent, Brandt semigroups and their generalization. Complete discussion of two examples and an idea for a new concept conclude the paper.