Some results of reverse derivation on prime and semiprime Γ-rings
Discussiones Mathematicae. General Algebra and Applications, Tome 35 (2015) no. 1, pp. 53-58.

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In the present paper, it is introduced the definition of a reverse derivation on a Γ-ring M. It is shown that a mapping derivation on a semiprime Γ-ring M is central if and only if it is reverse derivation. Also it is shown that M is commutative if for all a,b ∈ I (I is an ideal of M) satisfying d(a) ∈ Z(M), and d(a ∘ b) = 0.
Keywords: Prime Γ-rings, semiprime Γ-rings, derivations, reverse derivations
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Suliman, Neshtiman. Some results of reverse derivation on prime and semiprime Γ-rings. Discussiones Mathematicae. General Algebra and Applications, Tome 35 (2015) no. 1, pp. 53-58. http://geodesic.mathdoc.fr/item/DMGAA_2015_35_1_a4/

[1] W.E. Barness, On the Γ-rings of Nobusawa, Pacific J. Math. 18 (3) (1966) 411-422.

[2] M. Bresar and J. Vukman, On some additive mappings in rings with involution, Aequation Math. 38 (1989) 178-185. doi: 10.1007/BF01840003

[3] Md. F. Hoque and A.C. Paul, On centralizers of semiprime gamma rings, Intr. Math. Forum 6 (13) (2011) 627-638.

[4] S. Kyuno, On prime gamma rings, Pacific J. Math. 75 (1978) 185-190.

[5] L. Luh, On the theory of simple Gamma rings, Michigan Math. J. 16 (1969) 576-584. doi: 10.1307/mmj/1029000167

[6] N. Nobusawa, On a generalization of the ring theory, Osaka J. Math. 1 (1964) 81-89.

[7] M. Sapanci and A. Nakajima, A note on gamma rings, Turkish J. Math. 20 (1996) 463-465.

[8] M. Soytürk, The commutativity in prime gamma rings with Derivation, Turkish J. Math. 18 (1994) 149-155.