Biorder-preserving coextensions of fundamental semigroups

Abstract

In any extension theory for semigroups one must determine the basic building blocks and then discover how they fit together to create more complicated semigroups. For example, in group theory the basic building blocks are simple groups. In semigroup theory however there are several natural choices. One that has received considerable attention, particularly since the seminal work on inverse semigroups by Munn ([14, 15]), is the notion of a fundamental semigroup. A semigroup is called fundamental if it cannot be [shrunk] homomorphically without collapsing some of its idempotents (see below for a precise definition).