On Generalized (Sigma,Tau)-Derivations in 3-Prime Near-Rings

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Published: Sep 10, 2020
DOI: https://doi.org/10.5556/j.tkjm.51.2020.1829
Keywords:
Near-Rings Semigroup Ideal (σ τ)-Derivation Generalized (σ

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Emine Koç
Cumhuriyet University
https://orcid.org/0000-0002-8328-4293

Abstract

Let N be a 3-prime left near-ring with multiplicative center Z, f  be a generalized (σ,τ)- derivation on N with associated (σ,τ)-derivation d and I be a semigroup ideal of N. We proved that N must be a commutative ring if f(I)⊂Z  or f act as a homomorphism or f act as an anti-homomorphism.

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How to Cite
Koç, E. (2020). On Generalized (Sigma,Tau)-Derivations in 3-Prime Near-Rings. Tamkang Journal of Mathematics, 51(1), 1–12. https://doi.org/10.5556/j.tkjm.51.2020.1829
Issue
Vol. 51 No. 1 (2020)
Section
Papers
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This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Author Biography

Emine Koç, Cumhuriyet University

Cumhuriyet University 

Faculty Of Science

Department Of Mathematics

References

M. Ashraf, A. Ali and S.Ali, (σ,τ)-derivations on prime near-rings, Arch. Math.(Brno), 40(2004), 281–286.

A. Ali, H. E. Bell and R. Rani, (θ,φ)-Derivations as homomorphisms or as anti-homomorphisms on a near ring, Tamkang Journal of Math., 43 (2012), 385–390.

A. Ali, H. E. Bell and P. Miyan, Generalized derivations on prime near rings, Int. J. Math. Math Sci., 2013(2013), 1–5.

H. E. Bell and G. Mason, On derivations in near-rings, North-Holland Mathematics Studies, 137(1987), 31–35.

H. E. Bell, On derivations in near-rings II, Kluwer Academic Publ. Math. Appl. Dordr., 426(1997),191–197.

H. E. Bell and G. Mason, On derivations in near-rings and rings, Math. J. Okayama Univ., 34(1992),135–144.

M. Bresar, On the distance of the composition of two derivations to the generalized derivations, Glasgow Math. J., 33 (1991), 89–93.

O. Golbasi and N. Aydin, On near-ring ideals with (σ,τ)-derivation, Archivum Math. Bruno, Tomus, 43(2007), 87–92.

O. Golbasi, Some properties of prime near-rings with (σ,τ)−derivation, Sib. Math. J., 46(2005), 270–275.

O. Golbasi, On prime near-rings with genearlized (σ,τ)-derivation, Kyungpook Math. J., 45(2005), 249–254.

X. K. Wang, Derivations in prime near-rings, Proc. Amer. Math. Soc., 121(1994), 361-366.