Joshua Losh (University of Leeds) – Green's Relations and the Structure of Semigroups

Abstract: A semigroup is a set equipped with an associative binary operation. The definition is simple, but semigroups exhibit rich internal structure — one that is surprisingly different to groups. In this talk I will introduce the notion of a semigroups along with central notions to semigroup theory including Green's relations, key tools to understanding the structure of semigroups which partition elements according to how they generate ideals. This talk will give an overview of the area aimed at building intuition rather than deep technical knowledge.