Abstract
In the first part of the paper, we study the existence of derivations on a class of 3-prime near-rings. In the second part, we get some commutativity results for prime rings with generalized derivations.
References
[1] H. E. Bell, On derivations in near-rings. II, Nearrings, Nearfields and K-Loops (Hamburg 1995), Math. Appl. 426, Kluwer Acad. Publ., Dordrecht (1997), 191–197. 10.1007/978-94-009-1481-0_10Search in Google Scholar
[2] H. E. Bell, A. Boua and L. Oukhtite, Semigroup ideals and commutativity in 3-prime near rings, Comm. Algebra 43 (2015), no. 5, 1757–1770. 10.1080/00927872.2013.879161Search in Google Scholar
[3] H. E. Bell and G. Mason, On derivations in near-rings, Near-rings and near-fields (Tübingen, 1985), North-Holland Math. Stud. 137, North-Holland, Amsterdam (1987), 31–35. 10.1016/S0304-0208(08)72283-7Search in Google Scholar
[4] A. Boua, L. Oukhtite and H. E. Bell, Differential identities on semigroup ideals of right near-rings, Asian-Eur. J. Math. 6 (2013), no. 4, Article ID 1350050. 10.1142/S1793557113500502Search in Google Scholar
[5] A. A. M. Kamal and K. H. Al-Shaalan, Commutativity of rings and near-rings with generalized derivations, Indian J. Pure Appl. Math. 44 (2013), no. 4, 473–496. 10.1007/s13226-013-0025-8Search in Google Scholar
[6] A. A. M. Kamal and K. H. Al-Shaalan, Existence of derivations on near-rings, Math. Slovaca 63 (2013), no. 3, 431–448. 10.2478/s12175-013-0107-4Search in Google Scholar
[7] A. A. M. Kamal and K. H. Al-Shaalan, Commutativity of near-rings with derivations, Algebra Colloq. 21 (2014), no. 2, 215–230. 10.1142/S1005386714000170Search in Google Scholar
[8] A. A. M. Kamal and K. H. Al-Shaalan, Nonexistence of nonzero derivations on some classes of zero-symmetric 3-prime near-rings, Ukrainian Math. J. 66 (2014), no. 3, 473–478, Reprint of Ukraïn. Mat. Zh. 6 (2014), no. 3, 420–424. 10.1007/s11253-014-0945-4Search in Google Scholar
[9] J. D. P. Meldrum, Near-Rings and Their Links with Groups, Research Notes in Math. 134, Pitman, Boston, 1985. Search in Google Scholar
[10] G. Pilz, Near-Rings. The Theory and Its Application, 2nd ed., North-Holland Math. Stud. 23, North-Holland Publishing, Amsterdam, 1983. Search in Google Scholar
[11] X. K. Wang, Derivations in prime near-rings, Proc. Amer. Math. Soc. 121 (1994), no. 2, 361–366. 10.1090/S0002-9939-1994-1181177-7Search in Google Scholar
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