Homomorphisms of planar nearrings

Abstract

This dissertation is about two types of nearring: the planar nearring and the partite nearring. The planar nearring is best known for its connection with block designs and the partite nearring is a generalization of the planar nearring which is useful to have when studying homomorphisms. After defining and describing partite nearrings we look at ideals and homomorphisms. We see that homomorphisms defined on partite nearrings always have "associated homomorphisms." We also look at several theorems that tell us when a function defined on a partite nearring is a nearring homomorphism. In the final section we look at a particular type of "vector-space-generated" planar nearring and describe the group of automorphisms on that nearring.