Polynomial Near-Rings: Polynomials with Coefficients from a Near-Ring

Abstract

In 1987, A. P. J. van der Walt [1] overcame the difficulties caused by the lack of one distributive law in near-rings in order to create matrix near-rings with the property that when the near-ring is a ring, the matrix near-ring is the usual matrix ring. By an approach similar to that used by A. P. J. van der Walt we introduce in this paper a new polynomial near-ring with coefficients from a near-ring and derive some of its properties. Similar to van der Walt’s matrix near-ring work, when the coefficient near-ring is a ring, our polynomial near-ring coincides with the usual polynomial ring.