Date of Award
Doctor of Philosophy (PhD)
John A. Hildebrant
A semigroup has the congruence extension property (CEP) provided that each congruence on each subsemigroup can be extended to the semigroup. This property, along with the ideal extension property (IEP) and the group congruence extension property (GCEP) are studied in this work. Whether each of these properties is productive, hereditary or preserved by homomorphisms is determined (except for the homomorphic property for CEP). Conditions under which the homomorphic image of a semigroup with CEP has CEP are established. Disruptive element and disruptive pair theory is developed and shown to be an important concept in the study of CEP and IEP. Properties of semigroups with CEP are sought. It is proved that each semigroup with CEP has index less than four, and that this is both necessary and sufficient for a cyclic semigroup to have CEP. It is established that a group has CEP if and only if it is a torsion group with GCEP. In particular, an abelian group has CEP if and only if it is a torsion group.
Garcia, Josefa I., "The Congruence Extension Property for Algebraic Semigroups." (1988). LSU Historical Dissertations and Theses. 4638.