Research Article
Year 2019,
Volume: 40 Issue: 4, 838 - 845, 31.12.2019
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.
References
- [1] N. Nobusawa, On a generalization of the ring theory, Osaka J. Math., 1 (1964) 81-89.
- [2] W. E. Barnes, On the gamma Nobusawa, Pacific J. Math., 18 (1966) 411-422.
- [3] M.R. Hestenes, On a ternary algebra, Scripta Math., 29 (1973) 253-272.
- [4] O. Loos, Assoziative Triplesysteme, Manuscripta Math., 7 (1972) 103-112.
- [5] W.G. Lister, Ternary rings, Trans. Amer. Math. Soc., 154 (1971) 37-55.
- [6] R. N. Mukherjee Some results on Γ-rings, Indian J. pure appl. Math., 34 (2003) 991-994 . [7] S. Kyuno, On prime gamma rings, Pacific J. Math., 75 (1978) 185-190.
- [8] W. S. Martindale III, When are multiplicative mappings additive?, Proc. Amer. Math. Soc., 21 (1969) 695-698.
- [9] B. L. M. Ferreira, Multiplicative derivation of gamma rings, Algebra, Groups and Geometries, 34 (2017) 401-406.
- [10] B. L. M. Ferreira, Additivity of elementary maps on gamma ring, Extracta Mathematicae, 34 (2019) 61-76.
Year 2019,
Volume: 40 Issue: 4, 838 - 845, 31.12.2019
Abstract
References
- [1] N. Nobusawa, On a generalization of the ring theory, Osaka J. Math., 1 (1964) 81-89.
- [2] W. E. Barnes, On the gamma Nobusawa, Pacific J. Math., 18 (1966) 411-422.
- [3] M.R. Hestenes, On a ternary algebra, Scripta Math., 29 (1973) 253-272.
- [4] O. Loos, Assoziative Triplesysteme, Manuscripta Math., 7 (1972) 103-112.
- [5] W.G. Lister, Ternary rings, Trans. Amer. Math. Soc., 154 (1971) 37-55.
- [6] R. N. Mukherjee Some results on Γ-rings, Indian J. pure appl. Math., 34 (2003) 991-994 . [7] S. Kyuno, On prime gamma rings, Pacific J. Math., 75 (1978) 185-190.
- [8] W. S. Martindale III, When are multiplicative mappings additive?, Proc. Amer. Math. Soc., 21 (1969) 695-698.
- [9] B. L. M. Ferreira, Multiplicative derivation of gamma rings, Algebra, Groups and Geometries, 34 (2017) 401-406.
- [10] B. L. M. Ferreira, Additivity of elementary maps on gamma ring, Extracta Mathematicae, 34 (2019) 61-76.
There are 9 citations in total.
Details
| Primary Language | English |
|---|---|
| Journal Section | Natural Sciences |
| Authors | |
| Publication Date | December 31, 2019 |
| Submission Date | July 15, 2019 |
| Acceptance Date | November 4, 2019 |
| Published in Issue | Year 2019Volume: 40 Issue: 4 |