Generalized (α, β)-derivations in 3-prime near-rings

Boua, Abdelkarim; Abdelwanis, Ahmed

doi:10.1080/09720529.2021.1985801

Open Access Research Article

Generalized (α, β)-derivations in 3-prime near-rings

^*Abdelkarim BouaCorresponding authorabdelkarimboua@yahoo.fr; karimoun2006@yahoo.frPolydisciplinary Faculty Sidi Mohammed Ben Abdellah UniversityDepartment of Mathematics Sidi Mohamed Ben Abdellah University Polydisciplinary Faculty of Taza (FPT) Laboratory of Engineering Sciences (LSI)Fez, Taza, MoroccoView full profile → , Ahmed Abdelwanisayunis@sci.cu.edu.egDepartment of Mathematics Faculty of Science Cairo UniversityGiza, Giza, 12613, Egypt0000-0001-5236-5966View full profile →

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pp. 2139–2151Vol. 26Issue 8December 2023DOI: 10.1080/09720529.2021.1985801 Crossmark XML

Received:: 01 Dec 2020
Accepted:: 01 May 2021
Published Online:: 24 May 2022
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-1412
Pages:: 2139–2151

Abstract

Let be a 3-prime near-ring and are endomorphisms. In this paper, we generalize a few results concerning generalized derivations and two sided α -generalized derivations of 3-prime near rings to generalized (α, β) -derivations. Cases demonstrating the need of the 3-primeness speculation is given. When (resp. ), one can easily obtain the main results of [1] (resp. [4]).

Keywords

Commutativity Generalized (α β)-derivations 3-Prime near-rings

Subject Classifications

16N6016W2516Y30

References

[1] A. Y. Abdelwanis, Applications of two sided a-generalized derivations to 3-prime near-rings, Comm. Alg., 45 (2017), 4631-4645.
[2] M. Ashraf, A. Ali & S. Ali, (,)st-derivations on prime near-rings, Arch. Math., 40 (3) (2004), 281-286.
[3] H. E. Bell, On derivations in near-rings. Vol. II. In: Nearrings, Nearfields and K-loops (Hamburg, 1995) Math. Appl., Vol. 426. Dordrecht: Kluwer Acad. Publ., (1997), 191-197.
[4] H. E. Bell, A. Boua & L. Oukhtite, Semigroup ideals and commutativity in 3-prime near-rings, Comm. Alg., 43 ( 2015), 1757-1770.
[5] A. Boua, Lahcen Oukhtite & Abderrahmane Raji, Jordan ideals and derivations in prime near-rings Comment. Math. Univ. Carolin., 55 (2) (2014), 131-139.
[6] A. Boua, Commutativity of near-rings with certain constrains on Jordan ideals. Bol. Soc. Paran. Mat. 36 (4) (2018), 159-170.
[7] A. Boua, Commutativity of Jordan ideals in 3-prime near-rings with derivations, Commun. Korean Math. Soc. 33 (2018), No. 1, pp. 37-44, https://doi.org/10.4134/CKMS.c170015.
[8] En-guady, A., Boua, A. & Farhan, E, Some functional identities on near-rings involving Jordan ideals and left generalized derivations. Iraqi journal of science, 62 (6) (2021), 1961-1967.
[9] A. Boua & E. Farhan, Generalized derivations on near-rings with identities, Journal of Discrete Mathematical Sciences and Cryptography, (In press).
[10] Ö. Gölbasi, Notes on prime near-rings with generalized derivation, South. Asian Bull. Math., 30 (2006), 49-54.
[11] Ö. Gölbasi & N. Aydin, On near-ring ideals with (,)st-derivation, Arch. Math., 43 (2007), 87-92.
[12] S. Huang & Ö. Gölbasi, Notes on Prime Near-Rings with Generalized (,)st-Derivations, South. Asian Bull. Math., 36 (2012), 353-361.
[13] E. M. Khazil, Orthogonal generalized higher derivations in semi prime gamma near-rings, Journal of Discrete Mathematical Sciences and Cryptography, 23 (5) (2020), 1009-1020, DOI: 10.1080/09720529.2020.1723933
[14] E. C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc., 8 (1957), 1093-1100. https://doi.org/10.1090/s0002-9939-1957-0095863-0

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