Topological rings, homogeneous functions, and primeness

摘要

For 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: M-R(G)={f: GGf(ga)=f(g)a for all aR, gG}. In the special case that R is a topological ring and G is a topological R-module, we study N-R(G): ={fM(R)(G)f is continuous}. In particular, we investigate primeness of the near-ring N-R(G) of continuous homogeneous maps on G.