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2018•International Journal of Research -GRANTHAALAYAHOpen access

THE COMMUTATIVITY OF PRIME NEAR RINGS

Afrah Mohammad Ibraheem

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Abstract

Let N be a near-ring, and σ be an automorphisms of N. An additive mapping d from a near-ring N into itself is called a reverse σ-derivation on N if d (xy) = d(y) x + σ(y) d(x), holds for all x, y∈ N. In this paper, we shall investigate the commutativity of N by a reverse σ-derivation d satisfied some properties, when N is a prime ring.

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Let N be a near-ring, and σ be an automorphisms of N. An additive mapping d from a near-ring N into itself is called a reverse σ-derivation on N if d (xy) = d(y) x + σ(y) d(x), holds for all x, y∈ N. In this paper, we shall investigate the commutativity of N by a reverse σ-derivation d satisfied some properties, when N is a prime ring.

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Available abstract

Let N be a near-ring, and σ be an automorphisms of N. An additive mapping d from a near-ring N into itself is called a reverse σ-derivation on N if d (xy) = d(y) x + σ(y) d(x), holds for all x, y∈ N. In this paper, we shall investigate the commutativity of N by a reverse σ-derivation d satisfied some properties, when N is a prime ring.

Key concepts: Automorphism, Prime (order theory), Ring (chemistry), Commutative property, Commutative ring, Mathematics, Pure mathematics, Prime ring

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