Multiplicative Mappings of Gamma Rings

Year 2019, Volume: 40 Issue: 4, 838 - 845, 31.12.2019

Bruno Ferreira Ruth N. Ferreira

https://doi.org/10.17776/csj.592101

Cited By: 1

Abstract

Let Mi and Γi (i = 1, 2) be abelian groups such that Mi is a Γi-ring.
An ordered pair (ϕ, φ) of mappings is called a multiplicative isomorphism
of M1 onto M2 if they satisfy the following properties: (i) ϕ is a bijective
mapping from M1 onto M2, (ii) φ is a bijective mapping from Γ1 onto
Γ2 and (iii) ϕ(xγy) = ϕ(x)φ(γ)ϕ(y) for every x, y ∈ M1 and γ ∈ Γ1. We
say that the ordered pair (ϕ, φ) of mappings is additive when ϕ(x + y) =
ϕ(x) + ϕ(y), for all x, y ∈ M1. In this paper we establish conditions on
M1 that assures that (ϕ, φ) is additive.

Keywords

Multiplicative mappings, , Additivity, , Gamma rings.

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