Primitive inverse semigroups of left I-quotients

TL;DR

This paper characterizes semigroups that possess a primitive inverse semigroup of left I-quotients, focusing on the structure and properties of such semigroups within inverse semigroup theory.

Contribution

It provides a new characterization of semigroups with primitive inverse semigroup of left I-quotients, expanding understanding of their algebraic structure.

Findings

Characterization of semigroups with primitive inverse I-quotients

Conditions under which a semigroup admits such a structure

Insights into the algebraic properties of these semigroups

Abstract

A subsemigroup $S$ of an inverse semigroup $Q$ is a left I-order in $Q$, if every element in $Q$ can be written as $a^{-1}b$ where $a, b \in S$ and $a^{-1}$ is the inverse of $a$ in the sense of inverse semigroup theory. We study a characterisation of semigroups which have a primitive inverse semigroup of left I-quotients.