Abstract
In the present paper, we investigate the notion of generalized derivation satisfying certain algebraic identities in 3-prime near-ring N which forces N to be a commutative ring. Moreover, an example proving the necessity of the primeness of N is given.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bell, H.E.: On prime near-rings with generalized derivation. Int. J. Math. Math. Sci., Article ID 490316, (5 pages) (2008)
Bell, H.E.: On Derivations in Near-Rings II. Kluwer Academic Publishers, Netherlands (1997)
Bell, H.E., Argaç, N.: Derivations, products of derivations and commutativity in near-rings. Algebra Colloq. 8, 399–407 (2001)
Bell, H.E., Mason, G.: On derivations in near-rings. North-Holand Math. Stud. 137, 31–35 (1987)
Boua, A., Oukhtite, L., Bell, H.E.: Differential identities on semigroup ideals of right near-rings. Asian Eur. J. Math. 6, 1350050 (8 pages) (2013)
Daif, M.N., Bell, H.E.: Remarks on derivations on semiprime rings. Int. J. Math. Math. Sci. 15, 205–206 (1992)
Gölbaşi, Ö.: Notes on prime near-rings with generalized derivation. Southeast Asian Bull. Math. 30, 49–54 (2006)
Pilz, G.: Near-Rings, vol. 23, 2nd edn. North-Holland Math. Stud. (1983)
Wang, X.K.: Derivations in prime near-rings. Proc. Am. Math. Soc. 121, 361–366 (1994)
Acknowledgments
I wish to express my deep gratitude and very indebtedness to the referee for very fruitful discussions, constructive comments, remarks and suggestions on the manuscript.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Raji, A. Results on 3-prime near-rings with generalized derivations. Beitr Algebra Geom 57, 823–829 (2016). https://doi.org/10.1007/s13366-015-0267-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13366-015-0267-1