Multiplicative Mappings of Gamma Rings
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
References
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Details
Primary Language
English
Subjects
-
Journal Section
Research Article
Publication Date
December 31, 2019
Submission Date
July 15, 2019
Acceptance Date
November 4, 2019
Published in Issue
Year 2019 Volume: 40 Number: 4