On the Structure of σ_(1 )Near - Rings

Abstract

If, in a ring (N, +, ∙) we ignore the commutativity of ‘+’ and one of the distributive laws, (N, +, ∙) becomes a Near-Ring. If we do not stipulate the left distributive law, (N, +, ∙) is a right near-ring. This research aims to introduce the concept of σ_1near-ring. N is called σ_1near - ring if N is a right near-ring and xy^2=yxyfor all x,y∈N .The element wise characterization for σ_1near-ring will be investigated and shall establish theorems and properties in this near - ring.