In this paper, we consider graded near-rings over a monoid G as a generalizations of graded rings over groups. We introduce certain innovative graded prime ideals and study some of its basic properties over graded near-rings.

Graded Prime Ideals Over Graded Near Ring

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.

Generalizations Of Graded Prime Ideals Over Graded Near Rings

In this paper, we consider graded near-rings over a monoid G as generalizations of graded rings over groups, and study some of their basic properties. We give some examples of graded near-rings having various interesting properties, and we dene and study the G op -graded ring associated to a G-graded abelian near-ring, where G is a left cancellative monoid and G op is its opposite monoid. We also compute the graded ring associated to the graded near-ring of polynomials (over a commutative ring R) whose constant term is zero.

Graded near-rings

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On the category of near-rings

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Graded near-rings

On the category of near-rings