Generalizations Of Graded Prime Ideals Over Graded Near Rings

TL;DR

This paper introduces and explores new types of graded weakly prime and almost prime ideals in graded near-rings, extending the concept of graded prime ideals from graded rings to a broader algebraic context.

Contribution

It generalizes the notions of graded prime ideals to graded near-rings and investigates their properties and relationships.

Findings

Introduction of graded weakly prime ideals

Definition of graded almost prime ideals

Extension of properties of prime ideals to near-ring context

Abstract

This paper considers graded near-rings over a monoid G as a generalizations of the graded rings over groups, introduce certain innovative graded weakly prime ideals and graded almost prime ideals as a generalizations of graded prime ideals over graded near-rings, and explore their various properties and their generalizations in graded near-rings.