Some algebraic identities in 3-prime near-rings

  • A. Boua Sidi Mohamed Ben Abdellah Univ., Fez, Morocco
  • M. Ashraf Aligarh Muslim Univ., India
Keywords: prime near-rings

Abstract

We extend the domain of applicability of the concept of $(1, \alpha)$-derivations in $3$-prime near-rings by analyzing the structure and commutativity of near-rings admitting $(1, \alpha)$-derivations satisfying certain differential identities.

References

Ashraf, Mohammad; Ali, Shakir. On $(sigma,tau)$-derivations of prime near-rings. II. Sarajevo J. Math. 4(16) (2008), no. 1, 23--30. MR2428485

Bell, Howard E.; Mason, Gordon. On derivations in near-rings. Near-rings and near-fields (Tuebingen, 1985), 31--35, North-Holland Math. Stud., 137, North-Holland, Amsterdam, 1987. doi: 10.1016/S0304-0208(08)72283-7

Bell, Howard E. On derivations in near-rings. II. Nearrings, nearfields and $K$-loops (Hamburg, 1995), 191--197, Math. Appl., 426, Kluwer Acad. Publ., Dordrecht, 1997. doi: 10.1007/978-94-009-1481-0_10

Bell, H. E.; Boua, A.; Oukhtite, L. Semigroup ideals and commutativity in 3-prime near rings. Comm. Algebra 43 (2015), no. 5, 1757--1770. doi: 10.1080/00927872.2013.879161

A. Boua, L. Oukhtite, Semiderivations satisfying certain algebraic identities on prime near-rings, Asian-Eur. J. Math., 6, № 3 (2013), 8 p., doi: 10.1142/S1793557113500435

Pilz, Gunter. Near-rings. The theory and its applications. Second edition. North-Holland Mathematics Studies, 23. North-Holland Publishing Co., Amsterdam, 1983. {rm xv}+470 pp. ISBN: 0-7204-0566-1 MR0721171

Wang, Xue Kuan. Derivations in prime near-rings. Proc. Amer. Math. Soc. 121 (1994), no. 2, 361--366. doi: 10.2307/2160409

Samman, M.; Oukhtite, L.; Raji, A.; Boua, A. Two sided $alpha$-derivations in 3-prime near-rings. Rocky Mountain J. Math. 46 (2016), no. 4, 1379--1393. doi: 10.1216/RMJ-2016-46-4-1379

Published
15.01.2020
How to Cite
Boua A., and Ashraf M. “Some Algebraic Identities in 3-Prime Near-Rings”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, no. 1, Jan. 2020, pp. 36-45, http://umj.imath.kiev.ua/index.php/umj/article/view/2324.
Section
Research articles