Date of Award
Doctor of Philosophy (PhD)
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.
Dent, Topaz, "Clones of Finite Idempotent Algebras with Strictly Simple Subalgebras" (2011). Mathematics Graduate Theses & Dissertations. 3.