Annihilator Conditions on Polynomials over Modules

Let R be a ring with unity and M be a right R-module. The system M[x] forms a left near R[x]-module under addition and substitution operations. In this paper we extend the study of annihilator conditions on nearring of polynomials to left near R[x]-module M[x], when M is a reduced Baer module. Also, we give a characterization of reduced modules. As a corollary we obtain some results of Birkenmeier and Huang [3].