On approximate n-ring homomorphisms and n-ring derivations

M. Eshaghi Gordji

paper

On approximate n-ring homomorphisms and n-ring derivations

arXiv:0812.5024

Abstract

Let $A, B$ be two rings and let $X$ be an $A -$ module. An additive map $h : A \to B$ is called n-ring homomorphism if $h (Π_{i = 1}^{n} a_{i}) = Π_{i = 1}^{n} h (a_{i}),$ for all $a_{1}, a_{2}, ..., a_{n} \in A$ . An additive map $D : A \to X$ is called $n$ -ring derivation if $D (Π_{i = 1}^{n} a_{i}) = D (a_{1}) a_{2} ... a_{n} + a_{1} D (a_{2}) a_{3} ... a_{n} + ... + a_{1} a_{2} ... a_{n - 1} D (a_{n}),$ for all $a_{1}, a_{2}, ..., a_{n} \in A$ . In this paper we investigate the Hyers-Ulam-Rassias stability of $n$ -ring homomorphisms and n-ring derivations.

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