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 define and study the Gop-graded ring associated to a G-graded abelian near-ring, where G is a left cancellative monoid and Gop 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.

We consider the category of near-rings and study some categorical permanence properties. We investigate the connection between the concepts of monomorphism and, respectively, epimorphism of near-rings and the concepts of injective and, respectively, surjective morphism of near-rings. We also present some interesting properties of epimorphisms in the category of near-rings.

No abstract

No abstract