Volume 23 • Number 1 • 2000   R. Balakrishnan and S. Suryanarayanan Abstract. In page 297 of Pilz[4] a right near-ring N is called a near-ring if xN=xNx(Nx=xNx) for all x in N. Szasz, Frence, in [6] calls a ring N, with the property xN=xNx for all x in N, a -ring. We shall, in this paper, refer to a near-ring N with the property xN=xNx for all x in N, a near-ring. Motivated by these concepts we introduce Pk and Pk' near-rings (Definition 2.1). We further generalize these concepts by introducing Pk(r,m) and Pk'(r,m) near-rings (Definition 3.1). We discuss the properties of all these newly introduced structures in detail. We also obtain complete charcterisations and structure theorems for such near rings. Full text: PDF