Topological rings, homogeneous functions, and primeness

Abstract

ABSTRACTFor any group G such that G is a right R-module for some ring R, the elements of R act on G as endomorphisms and we obtain the near-ring of R-homogeneous maps on G: MR(G) = {f: G → G|f(ga) = f(g)a for all a ∈ R, g ∈ G}. In the special case that R is a topological ring and G is a topological R-module, we study NR(G): = {f ∈ MR(G)|f is continuous}. In particular, we investigate primeness of the near-ring NR(G) of continuous homogeneous maps on G.