## African Diaspora Journal of Mathematics

### On Derivations of Prime Near-Rings

#### Abstract

In this paper we investigate derivations satisfying certain differential identities on 3-prime near-rings, and we provide examples to show that the assumed restrictions cannot be relaxed.

#### Article information

Source
Afr. Diaspora J. Math. (N.S.), Volume 14, Number 1 (2012), 65-72.

Dates
First available in Project Euclid: 18 July 2013

Mathematical Reviews number (MathSciNet)
MR2805230

Zentralblatt MATH identifier
1280.16047

Subjects
Primary: 16Y30, 13N15, 15A27

#### Citation

Bell, H. E.; Boua, A.; Oukhtite, L. On Derivations of Prime Near-Rings. Afr. Diaspora J. Math. (N.S.) 14 (2012), no. 1, 65--72. https://projecteuclid.org/euclid.adjm/1374153556

#### References

• M. Ashraf and N. Rehman, On commutativity of rings with derivations. Result. Math. 12 (2002), 3-8.
• M. Ashraf and A. Shakir, On $(\sigma, \tau)$-derivations of prime near-rings. Arch. Math. (Brno) 40 (2004), no. 3, 281-286.
• M. Ashraf and A. Shakir, On $(\sigma, \tau)$-derivations of prime near-rings-II. Sarajevo J. Math. 4 (2008), no. 16, 23-30.
• K. I. Beidar, Y. Fong and X. K. Wang, Posner and Herstein theorems for derivations of 3-prime near-rings. Comm. Algebra 24 (1996), no. 5, 1581-1589.
• H. E. Bell, Certain near-rings are rings. J. London Math. Soc. 4 (1971),264-270.
• H. E. Bell, On derivations in near-rings II. Kluwer Academic Publishers Netherlands (1997), 191-197.
• H. E. Bell and M. N. Daif, Commutativity and strong commutativity preserving maps. Canad. Math. Bull. 37 (1994), 443-447.
• H. E. Bell and G. Mason, On derivations in near-rings. North-Holland Mathematics Studies 137 (1987), 31-35.
• H. E. Bell and G. Mason, On derivations in near-rings and rings. Math. J. Okayama Univ. 34 (1992), 135-144.
• A. Boua and L. Oukhtite, Derivations on prime near-rings. Int. J. Open Probl. Comput. Sci. Math. 4 (2011), no. 2, 162-167.
• M. N. Daif and H. E. Bell, Remarks on derivations on semiprime rings. Int. J. Math. & Math. Sci. 15 (1992), 205-206.
• A. A. Klein, A new proof of a result of Levitzki. Proc. Amer. Math. Soc. 81 (1981), no. 1, 8.
• X. K. Wang, Derivations in prime near-rings. Proc. Amer. Math. Soc. 121 (1994), 361-366.