ON AN ARMENDARIZ-TYPE CONDITION IN POLYNOMIAL NEAR-RINGS

Let R be an associative ring with unity. In this paper we introduce the notion of an Rmendariz-type condition in the class of near-rings. We then show that Armendariz-type condition is a generalization of reduced condition. We also show that a ring satisfying the Armendariz-type condition is abelian and hence all its idempotent elements are central. We then initiate the study of some annihilator conditions on polynomial near-rings. we then study near-rings with Baer condition and near-rings with p.p. condition which are somewhat different from the ring cese, and extends a results of Armendariz to polynomial near-rings. As a consequence we extend results of to the more general case where R is not necessarily commutative.

Keywords:

polynomial near-ring , Baer near-ring , Armendariz-type ring , reduced ring