Date of Award
Summer 1994
Document Type
Dissertation - Restricted
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics, Statistics and Computer Science
First Advisor
Pastijn, Francis
Second Advisor
Byleen, Karl
Third Advisor
Jones, Peter
Abstract
The class CS, of all semigroups that are embeddable in completely simple semigroups forms a quasivariety. That is, it is the class of all semigroups that satisfy some set of implications. The problem of obtaining a basis of this set of implications, and determining whether or not CS can be defined by a finite set of implications is treated. As special cases, various subquasivarieties of CS are considered, and for each of these quasivarieties similar questions concerning the basis of implications are treated. Another special case is where semigroups S that are embeddable in completely simple semigroups of right quotients of S are considered, and characterizations for those Sare presented in terms of the free completely simple semigroup on S. In a broader context, the problem of finding a basis of implications for the quasivariety consisting of semigroups that are embeddable in V-bands of abelian groups,where V is a variety of bands, is studied. "formula", the quasivariety of all semigroups that can be embedded in semilattices of nilpotent groups of class n is also considered to obtain a basis of implications for it. Solutions to all of these questions have been presented in this dissertation.