Boolean Orthogonalities For Near-rings

Cornish has developed a theory of Boolean orthogonalities for sets with an associated algebraic closure system of “ideals”, and applied it to reduced rings and semiprime rings. In this paper we apply the theory to near-rings and in particular to 3-somiprime near-rings. As one consequence, we identify some near-rings whose 3-semiprime ideals are intersections of 3-prime ideals. In the final section, we discuss local ideals and normality conditions for near-rings with a. Boolean orthogonality.