Near-rings of mappings on finite topological groups

Abstract

AbstractWhen G is a topological group, the set N(G) of continuous self-maps of G, and the subset N0(G) of those which fix the identity of G, are near-rings. In this paper we examine the (left) ideal structure of these near-rings when G is finite. N0(G) is shown to have exactly two maximal ideals, whose intersection is the radical. In the final section we investigate subnear-rings of N0(G) determined by certain continuous elements of the endomorphism near-ring.