On Complement and Supplement Ideals of Nearrings

Abstract

In this article we study complement ideals, and the dual concept of supplement ideals, in nearrings, both of which are generalizations of the concept of complement in a bounded modular lattice. We prove fundamental properties of complements and supplements in arbitrary nearrings. We then establish Galois connections between the ideal lattices of a nearring and of its matrix nearrings, yielding one-to-one correspondences between their respective complement and supplement ideals. We also define graphs associated with complement and supplement ideals of nearrings and study some of their combinatorial properties such as girth and clique number.