Introduction to fundamental semigroups

Speaker: David Easdown, University of Sydney

Abstract: In semigroup theory there are many natural candidates for "basic building blocks". The ones we will consider in this talk are semigroups which are fundamental, which means that they cannot be "shrunk" homomorphically without collapsing part of the "skeleton" of idempotents. These have been well studied within the class of regular semigroups, but little is known for possibly nonregular semigroups. I will try to convince you that every semigroup is a coextension of a fundamental semigroup in which the idempotent skeleton is maintained perfectly intact! So fundamental semigroups are indeed splendid candidates for a general extension theory of semigroups. In a later talk Brad Roberts will produce a large class of (possibly nonregular) fundamental semigroups built from biordered sets.