Structure of 3-Prime Near Rings with Generalized (σ,τ)-n-Derivations
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Authors: A. ALI, A. BOUA AND I. UL HUQUE
DOI: 10.46793/KgJMat2306.891A
Abstract:
In this paper, we define generalized (σ,τ)-n-derivation for any mappings σ and τ of a near ring N and also investigate the structure of a 3-prime near ring satisfying certain identities with generalized (σ,τ)-n-derivation. Moreover, we characterize the aforementioned mappings.
Keywords:
3-prime near ring, semigroup ideal, (σ,τ)-n-derivations, generalized (σ,τ)-n-derivations.
References:
[1] H. E. Bell, On derivations in near rings II, in: G. Saad and M. J. Thomsen (Eds.), Nearrings, Nearfields and K-Loops, Springer, Dordrecht, 191–197. https://doi.org/10.1007/978-94-009-1481-0_10
[2] A. Boua, A. Y. Abdelwanis and A. Chillali, Some commutativity theorems for near-rings with left multipliers, Kragujevac J. Math. 44(2) (2020), 205–216. https://doi.org/10.46793/KgJMat2002.205B
[3] A. Boua and M. Ashraf, Some algebraic identities in 3-prime near-rings, Ukrainian Math. J. 72(1) (2020), 39–51. https://doi.org/10.1007/s11253-020-01762-5
[4] Y. Ceven and M. A. Ozturk, Some properties of symmetric bi-(σ,τ)-derivations in near-rings, Commun. Korean Math. Soc. 22(4) (2007), 487–491. https://doi.org/10.4134/CKMS.2007.22.4.487
[5] J. Vukman, Identities with derivations and automorphisms on semiprime rings, Int. J. Math. Math. Sci. 7 (2005), 1031–1038. https://doi.org/DOI:10.1155/ijmms.2005.1031
[6] K. H. Park and Y. S. Jung, On permuting 3-derivations and commutativity in prime near rings, Commun. Korean Math. Soc. 25(1) (2010), 1–9. https://doi.org/10.4134/CKMS.2010.25.1.001
[7] M. Bresar, On skew commuting mappings of rings, Bull. Aust. Math. Soc. 47(2) (1993), 291–296. https://doi.org/10.1017/S0004972700012521
[8] M. A. Öztürk and H. Yazarli, A note on permuting tri-derivation in near ring, Gazi University Journal of Science 24(4) (2011), 723–729.
[9] M. A. Öztürk and Y. B. Jun, On trace of symmetric bi-derivations in near rings, International Journal of Pure and Applied Mathematics 17 (2004), 95–102.
[10] G. Pilz, Near-Rings: The Theory and its Applications, North Holland, New York, 1977.
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