ON GDG BOOLEAN NEAR – RINGS

ON GDG BOOLEAN NEAR – RINGS

Author Name : Dr. Navrang Manikrao

ABSTRACT

It is well known that Boolean rings have applications in computer science and partial order can be defined with which the Boolean ring becomes a complemented distributive lattices.

In this paper we introduce the concept of g d g Near – ring. Each d g near – ring is a g d g Near – ring. Examples of g d g Near – ring are given. It is well known that d g Boolean near – ring is a Boolean ring. But a g d g Boolean near – ring is in general need not be a Boolean ring.

As in the case of Boolean rings, partial order can be defined from g d g Boolean near – ring. If a g d g Boolean near – ring is a join or meet semi lattice, then it is a Boolean ring. An Interesting result is that a g d g Boolean near – ring is a disjoint union of mutually isomorphic distributive lattices each with a zero element. Many known results are consequences of above result.