Merhaba Misafir

Multiplicative mappings of gamma rings

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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.

Yayınlandığı Kaynak : Cumhuriyet Science Journal
  • Yıl : 2019
  • DOI : 10.17776/csj.592101
  • Cilt : 40
  • ISSN : 2587-2680
  • Sayı : 4
  • eISSN : 2587-246X
  • Sayfa Aralığı : 838-845
  • IO Kayıt No : 107154
  • Yayıncı : Cumhuriyet Üniversitesi