Department of Mathematics, Pope's college (Autonomous), Sawyerpuram–628251, Tamil Nadu
(Affiliated to Mannonmaniam Sundaranar University, Tirunelveli-627012)
Online published on 7 May, 2019.
In this paper we introduce the concept of near-rings in which every N-subgroup is an ideal. In [5], S. Suryanarayanan and R. Balakrishnan investigated a near-ring N in which every N-subgroup is invariant. Motivated by this concept, we probe into the properties of a near-ring N where every N-subgroup is an ideal. We discuss the properties of this newly introduced structure, and furnish a characterization and prove that all principal ideals with mate functions is a distributive lattice.
Near-ring, prime ideal, maximal ideal
