Date of Award

Spring 1-1-2011

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics

First Advisor

Agnes Szendrei

Second Advisor

Keith Kearnes

Third Advisor

Don Monk

Abstract

Abstract: We determine the clone of a finite idempotent algebra A that is not simple and has a unique nontrivial subalgebra S with more than two elements. Under these conditions, the proper subalgebras and the quotient algebra of A are finite idempotent strictly simple algebras of size at least 3 and it is known that such algebras are either affine, quasiprimal, or of a third classification. We focus on the first two cases. By excluding binary edge blockers from the relational clone when S is affine and by excluding ternary edge blockers from the relational clone together with an additional condition on the subuniverses of A2 when S is quasiprimal, we give a nice description of the generating set of the relational clone of A. Thus, by the Galois connection between operations and relations, we determine the clone of A.

Included in

Mathematics Commons

Share

COinS