Topology and Primary N-Groups

Abstract

A primary N-group is a compatible N-group without ring submodules and two non-zero submodules with zero intersection. A very natural zero set topology arises and an adaptation of this is used throughout the paper. Topological features are studied and these are related to algebraic properties of the nearring. Many surprising results are obtained. The last part of the paper is concerned with showing, that with connectedness, direct decomposition implies we are dealing with the reals. Furthermore, local compact-ness implies the nearring is a subnearring of the nearring of all zero-fixing continuous self maps on the reals.