Morita equivalence of inverse semigroups

TL;DR

This paper characterizes all inverse semigroups that are Morita equivalent to a given one by constructing specific inverse images of Rees matrix semigroups satisfying certain conditions.

Contribution

It introduces a method to construct all Morita equivalent inverse semigroups using maximum inverse images and McAlister conditions on sandwich matrices.

Findings

Provides a construction for Morita equivalence classes of inverse semigroups

Identifies McAlister conditions as key criteria for sandwich matrices

Establishes a framework for classifying inverse semigroups by Morita equivalence

Abstract

We describe how to construct all inverse semigroups Morita equivalent to a given inverse semigroup. This is done by taking the maximum inverse images of the regular Rees matrix semigroups over the inverse semigroup where the sandwich matrix satisfies what we call the McAlister conditions.