On two sided α-n-derivation in 3-prime near-rings
- 23 Downloads
Let N be a left near-ring and let α be a function of N. We introduce the notion of two sided α-n-derivation and prove that a prime zero symmetric near-ring involving α-n-derivations satisfying certain identities is a commutative ring.Also, some examples are given to shown that the 3-primeness condition in our results is not redundant.
Key words and phrasesprime near-ring derivation two sided α-n-derivation commutativity
Mathematics Subject Classification16N60 16W25 16Y30
Unable to display preview. Download preview PDF.
- 4.H. E. Bell and G. Mason, On derivations in near-rings, in: Near-rings and Near-fields (Tübingen, 1985), North-Holland Mathematics Studies, 137, North-Holland (Amsterdam, 1987), pp. 31–35.Google Scholar
- 6.H. E. Bell, On derivations in near-rings. II, in: Nearrings, nearfields and K-loops (Hamburg, 1995), Math. Appl., 426, Kluwer Acad. Publ. (Dordrecht, 1997), pp. 191–197.Google Scholar
- 11.Öztürk, M.A.: Permuting tri-derivations in prime and semiprime rings. East Asian Math. J. 15, 177–190 (1999)Google Scholar
- 13.Park, K.H.: On prime and semiprime rings with symmetric \(n\)-derivations. J. Chungcheong Math. Soc. 22, 451–458 (2009)Google Scholar