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Title:
Study of differential identities in $3$-prime near-rings
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Discussiones Mathematicae - General Algebra and Applications
Received: 2024-06-18 , Revised: 2024-09-26 , Accepted: 2024-09-27 , Available online: 2025-05-23 , https://doi.org/10.7151/dmgaa.1479
Abstract:
The main objective in the present paper is to describe the structure of a 3-prime near-ring N satisfy certain algebraic identities involving g-derivation. In addition, and to show the necessity of the different hypotheses used in our results, we will present at the end of this work examples which illustrate that the restrictions imposed are not superfluous.
Keywords:
3-prime near-rings, $g$-derivation, multipliers, commutativity
References:
- M. Ashraf and N. Rehman, On commutativity of rings withderivations, Results Math. 12 (2002) 3–8.
https://doi.org/10.1007/BF03323547 - H. E. Bell, A. Boua and L. Oukhtite, Semigroup ideals and commutativity in 3-prime near-rings, Comm. Algebra 43(5) (2015) 1757–1770.
https://doi.org/10.1080/00927872.2013.879161 - H. E. Bell, On Derivations in Near-Rings II, Kluwer Academic Publishers, Dordrecht (1997) 191-–197.
https://doi.org/10.1007/978-94-009-1481-0_10 - H. E. Bell, M. N. Daif, Commutativity and strong commutativity preserving maps, Can. Math. Bull. 37 (1994) 443–447.
https://doi.org/10.4153/CMB-1994-064-x - H. E. Bell, G. Mason, On derivations in near-rings and rings, Math. J. Okayama Univ. 34 (1992) 135–144.
- H. E. Bell and G. Mason, On derivations in near-rings, North-Holand Mathematics Studies 137 (1987) 31–35.
- A. Boua, and L. Taoufiq, Some algebraic results involving derivations in 3-prime near-rings, Indian J. Math 59(2) (2017) 147–160.
- A. Boua, L. Oukhtite and A. Raji, On generalized semiderivations in 3-prime near-rings, Asian-European Journal of Mathematics 9(2) (2016) p.1650036.
https://doi.org/10.1142/S1793557116500364 - M. N. Daif and H. E. Bell, Remarks on derivation on semiprime rings, Int. J. Math. Math. Sci. 15 (1992) 205–206.
- N. Divinsky, On commuting automorphisms of rings, Trans. Roy. Soc. Can. Sect. III. 49(3) (1955) 19–22.
- E. C. Posner, Derivations in prime rings, Proc. Am. Math. Soc. 8 (1957) 1093–1100.
https://doi.org/10.2307/2032686 - A. Raji, Results on 3-prime near-rings with generalized derivations, Beitrage zur Algebra und Geometrie 57(4) (2016) 823–829.
https://doi.org/10.1007/s13366-015-0267-1 - M. Samman, L. Oukhtite, A. Raji and A. Boua, Two sided $\alpha$-derivations in 3-prime near-rings, Rocky Mountain Journal of Mathematics 46(4) (2016) 1379–1393.
https://doi.org/10.1216/RMJ-2016-46-4-1379 - S. M. A. Zaidi, M. Ashraf, S. Ali, On Jordan ideals and left $(\theta,\theta)$-derivations in prime rings, Int. J. Math. Math. Sci. 37-40 (2004) 1957–1964.
https://doi.org/10.1155/S0161171204309075
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