On approximate n-ring homomorphisms and n-ring derivations

2008/12/30 by M. Eshaghi Gordji, Gordji, M. Eshaghi
Mathematics · #39B52 #39B72 #39B82 #46H25 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:39B52 #msc:39B72 #msc:39B82 #msc:46H25

paper · pdf · doi:10.48550/arxiv.0812.5024

arxiv created 2008/12/30 · arxiv updated 2009/12/01

Abstract

Let A,B be two rings and let X be an A-module. An additive map h: A→ B is called n-ring homomorphism if h(Πⁿ_i=1a_i)=Πⁿ_i=1h(a_i), for all a₁,a₂, ...,a_n ∈ A. An additive map D: A→ X is called n-ring derivation if D(Πⁿ_i=1a_i)=D(a₁)a₂... a_n+a₁D(a₂)a₃... a_n+... +a₁a₂... a_n-1D(a_n), for all a₁,a₂, ...,a_n ∈ \mathcal A. In this paper we investigate the Hyers-Ulam-Rassias stability of n-ring homomorphisms and n-ring derivations.

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