Algebra and Logic Seminar - 4/3/2015

Wednesday, 4 March 2015, 2:00 p.m.

Lecturer: Prof. Dr. Jörg Koppitz (Institute of Mathematics, Potsdam University, Germany)

Title: "Alternative varieties of completely regular semigroups"

Local: Room 1.13, Edifício VII
Faculdade de Ciências e Tecnologia, Quinta da Torre, Caparica

Abstract: It is well known that completely regular semigroups are semilattices of completely simple semigroups (Lallement 1967, Petrich 1974). If we choose as completely simple semigroups the class of rectangular bands then the variety of bands is characterized (M. Petrich). João Pedro Araújo and Michael Kinyon in 2014 characterize semigroups being semilattices of rectangular bands or groups with exponent 2 by so called alternative identities de…ned class. Such classes were …rst studied by E. S. Lyapin (1974) as power identity inclusions. These classes are also called alternative varieties. In 1985, A. E. Evseev investigated semigroups with some power identity inclusions. In this seminar, we will introduce the concept of alternative varieties as a generalization of varieties. We investigate the characterization of particular classes of completely regular semigroups (i.e. of semilattices of completely simple semigroups) by alternative varieties. We will discuss a couple of examples.