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http://dx.doi.org/10.7858/eamj.2020.010

LIE IDEALS AND COMMUTATIVITY OF 2-TORSION FREE SEMIPRIME RINGS WITH GENERALIZED DERIVATION  

Sogutcu, Emine Koc (Cumhuriyet University, Faculty of Science, Department of Mathematics)
Golbasi, Oznur (Cumhuriyet University, Faculty of Science, Department of Mathematics)
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Abstract
In this paper, we investigate commutativity of semiprime rings with a derivation which is strongly commutativity preserving and acts as a homomorphism or as an anti-homomorphism on a nonzero Lie ideal.
Keywords
semiprime ring; Lie ideal; derivation; generalized derivation;
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1 DAIF, M. N. and BELL, H. E., Remarks on derivations on semiprime rings, Internat J. Math. and Math. Sci., 15(1), (1992), 205-206.   DOI
2 HONGAN, M., REHMAN, N. and AL-OMARY R. M., Lie ideals and Jordan triple derivations in rings, Rend. Semin. Mat. Univ. Padova, 125, (2011), 147-156.   DOI
3 KOC, E., Some results in semiprime rings with derivation, Commun. Fac. Sci. Univ. Ank. Series A1, 62(1), (2013), 11-20.
4 POSNER, E. C., Derivations in prime rings, Proc Amer.Math.Soc., 8, (1957), 1093-1100.   DOI
5 REHMAN, N. andHONGAN, M., Generalized Jordan derivations on Lie ideals associate with Hochschild 2-cocycles of rings, Rend. Circ. Mat. Palermo, 60(3), (2011), 437-444.   DOI
6 SAMMAN, M.S., On strong commutativity-preserving maps, Internat J. Math. Math. Sci., 6,(2005), 917-923.   DOI
7 BRESAR, M., On the distance of the composition of two derivations to the generalized derivations, Glasgow Math. J., 33, (1991), 89-93.   DOI
8 ALI, A., YASEN, M. and ANWAR, M., Strong commutativity preserving mappings on semiprime rings, Bull. Korean Math. Soc., 43(4), (2006), 711-713.   DOI
9 ASHRAF, M., ALI, A. and RANI, R., On generalized derivations of prime rings, Southeast Asian Bull. of Math., 29, (2005), 669-675.
10 AWTAR, R.: Lie structure in prime rings with derivations, Publ. Math. Debrecen, 31, (1984), 209-215.
11 BELL, H. E. and KAPPE, L. C., Rings in which derivations satisfy certain algebraic conditions, Acta Math. Hungarica, 53, (1989), 339-346.   DOI
12 BERGEN, I., HERSTE˙IN, I. N. and KERRJ.W., Lie ideals and derivation of prime rings, J. of Algebra, 71, (1981), 259-267.   DOI