SOME COMMUTATIVITY THEOREMS OF PRIME RINGS WITH GENERALIZED (σ, τ)-DERIVATION

Title & Authors
SOME COMMUTATIVITY THEOREMS OF PRIME RINGS WITH GENERALIZED (σ, τ)-DERIVATION
Golbasi, Oznur; Koc, Emine;

Abstract
In this paper, we extend some well known results concerning generalized derivations of prime rings to a generalized ($\small{{\sigma}}$, $\small{{\tau}}$)-derivation.
Keywords
prime rings;derivations;generalized derivations;generalized ($\small{{\sigma}}$, $\small{{\tau}}$)-derivations;centralizing mappings;
Language
English
Cited by
1.
On Generalized ()-Derivations in Semiprime Rings, ISRN Algebra, 2012, 2012, 1
2.
A Note on the Commutativity of Prime Near-rings, Algebra Colloquium, 2015, 22, 03, 361
References
1.
N. Argac, A. Kaya, and A. Kisir, (${\sigma}$, ${\tau}$)-derivations in prime rings, Math. J. Okayama Univ. 29 (1987), 173-177.

2.
M. Ashraf, A. Asma, and R. Rekha, On generalized derivations of prime rings, Southeast Asian Bull. Math. 29 (2005), no. 4, 669-675.

3.
M. Ashraf, A. Asma, and A. Shakir, Some commutativity theorems for rings with generalized derivations, Southeast Asian Bull. Math. 31 (2007), no. 3, 415-421.

4.
N. Aydin and K. Kaya, Some generalizations in prime rings with (${\sigma}$, ${\tau}$)-derivation, Doga Mat. 16 (1992), no. 3, 169-176.

5.
H. E. Bell and M. N. Daif, On commutativity and strong commutativity-preserving maps, Canad. Math. Bull. 37 (1994), no. 4, 443-447.

6.
H. E. Bell and W. S. Martindale, Centralizing mappings of semiprime rings, Canad. Math. Bull. 30 (1987), no. 1, 92-101.

7.
M. Bresar, On the distance of the composition of two derivations to the generalized derivations, Glasgow Math. J. 33 (1991), no. 1, 89-93.

8.
M. Bresar, Commuting traces of biadditive mappings, commutativity-preserving mappings and Lie mappings, Trans. Amer. Math. Soc. 335 (1993), no. 2, 525-546.

9.
J. C. Chang, On (${\alpha}$, ${\beta}$)-derivations of prime rings, Chinese Journal Math. 22 (1991), no. 1, 21-30.

10.
M. N. Daif and H. E. Bell, Remarks on derivations on semiprime rings, Internat. J. Math. Math. Sci. 15 (1992), no. 1, 205-206.

11.
Q. Deng and M. Ashraf, On strong commutativity preserving mappings, Results Math. 30 (1996), no. 3-4, 259-263.