Limit Varieties Generated by Completely 0-Simple Semigroups

A variety of semigroups that is minimal with respect to being non-finitely based is said to be a limit variety. By Zorn’s Lemma, each non-finitely based variety contains at least one limit subvariety. Although many examples of non-finitely based varieties are known in the literature (see [3, 5]), explicit examples of limit varieties are very rarely discovered [1, 2, 4]. The objective of the present talk is to introduce a new infinite class of limit varieties. These varieties constitute all limit varieties generated by completely 0-simple semigroups and are each generated by a finite Rees matrix semigroup over a cyclic group of prime order. Subvarieties of these limit varieties will also be described.