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Topological rings,homogeneous functions,and primeness
Authors:G L Booth  K Mogae
Institution:Nelson Mandela Metropolitan University, Port Elizabeth, South Africa
Abstract: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: 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.
Keywords:Continuous  homogeneous function  near-ring  prime  topological ring
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