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Near-rings of polynomials and polynomial functions

Abstract In this paper we investigate near-rings of polynomials and polynomial functions. After some results which belong to universal algebra we turn our attention to the familiar case of polynomials and polynomial functions over a commutative ring with identity. We study the relation between ring- and near-ring homomorphisms, and the behaviour of polynomial near-rings when the ring splits into a direct sum. A discussion of the structure of these polynomial near-rings (radical, semisimplicity) finishes this paper. These investigations are motivated by Clay and Doi (1973).