Volume 50 | Number 5 | Year 2017 | Article Id. IJMTT-V50P542 | DOI : https://doi.org/10.14445/22315373/IJMTT-V50P542
In the present paper, we investigate the commutativity of 3-prime near-rings satisfying certain conditions and identities involving left generalized multiplicative derivations. Moreover, examples have been provided to justify the necessity of 3-primeness condition in the hypotheses of various results.
[1] Ashraf, M., Boua, A., Siddeeque, M.A., Generalized multiplicative derivations in 3-prime near-rings, Mathematica Slovaca, (2017), (To appear).
[2] Ashraf, M., Rehman, N., On commutativity of rings with derivations, Results Math, (2002), Vol. 42(1 - 2), 3 - 8.
[3] Bell, H.E., On prime near-rings with generalized derivations, International Journal of Mathematics and Mathematical Sciences, (2008), Article ID 490316, 5 pages.
[4] Bell, H.E., On derivations in near-rings II, Kluwer Academic Publishers Dordrecht, Vol. 426, (1997), 191 - 197.
[5] Bell, H.E., Boua, A., Oukhtite, L., Semigroup ideals and commutativity in 3-prime near-rings, Comm. Algebra, 43, (2015), 1757 - 1770.
[6] Bell, H.E. and Mason, G., On derivations in near-rings, Near-rings and Near-elds (G. Betsch editor), North-Holland / American Elsevier, Amsterdam, 137, (1987) , 31 - 35.
[7] Boua, A., Kamal A.A.M., Some results on 3-prime near-rings with derivations, Indian J. Pure Appl. Math., 47(4), (2016), 705 - 716.
[8] Boua, A., Oukhtite, L., On commutativity of prime near-rings with derivations, South East Asian Bull. Math., 37, (2013), 325 - 331.
[9] Golbasi., O:, On generalized derivations of prime near-rings, Hacet. J. Math. & Stat., 35(2), (2006), 173 - 180.
[10] Havala, B., Generalized derivations in rings, Comm. Algebra, 26, 1147 - 1166, (1998).
[11] Kamal, A.A.M. and Al-Shaalan, K. H., Existence of derivations on near-rings, Math. Slovaca, 63(3), (2013), 431 - 448.
[12] Meldrum, J.D.P., Near-rings and their links with groups, Res. Notes Math. 134, Pitman ( Advanced Publishing Program), Bostan, M.A., (1985).
[13] Pilz, G., Near-rings, 2nd ed., 23, North Holland /American Elsevier, Amsterdam, (1983).
[14] Wang, X.K., Derivations in prime near-rings, Proc. Amer. Math. Soc., 121, No.(2); (1994); 361 - 366.
Mohammad Aslam Siddeeque, "Generalized Multiplicative Derivations in Near-Rings," International Journal of Mathematics Trends and Technology (IJMTT), vol. 50, no. 5, pp. 252-260, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V50P542