POLARITIES FOR NEARRINGS

Abstract

We show that the left and right polar sets of a nearring N form complete bounded lattices P_R(N) and P_L(N). We consider properties of P_L(N) and its elements, which are ideals, when N is 3-semiprime. If in addition N is zero-symmetric we strengthen these results and use them to describe a class in which 3-semiprime nearrings are strongly 3-semiprime.