ON GENERALIZED JORDAN LEFT DERIVATIONS IN RINGS

Title & Authors
ON GENERALIZED JORDAN LEFT DERIVATIONS IN RINGS

Abstract
In this paper, we introduce the notion of generalized left derivation on a ring R and prow that every generalized Jordan left derivation on a 2-torsion free primp ring is a generalized left derivation on R. Some related results are also obtained.
Keywords
prime rings;generalized left derivation;generalized Jordan left derivation;
Language
English
Cited by
1.
LEFT JORDAN DERIVATIONS ON BANACH ALGEBRAS AND RELATED MAPPINGS,;;

대한수학회보, 2010. vol.47. 1, pp.151-157
1.
On generalized left derivations in rings and Banach algebras, Aequationes mathematicae, 2011, 81, 3, 209
2.
LEFT JORDAN DERIVATIONS ON BANACH ALGEBRAS AND RELATED MAPPINGS, Bulletin of the Korean Mathematical Society, 2010, 47, 1, 151
3.
On Lie Ideals and Generalized Jordan Left Derivations of Prime Rings, Ukrainian Mathematical Journal, 2014, 65, 8, 1247
4.
Generalized Jordan left derivations on semiprime algebras, Monatshefte für Mathematik, 2010, 161, 1, 77
5.
Generalized Jordan left derivations in rings with involution, Demonstratio Mathematica, 2012, 45, 4
6.
Generalized left derivations acting as homomorphisms and anti-homomorphisms on Lie ideal of rings, Journal of the Egyptian Mathematical Society, 2014, 22, 3, 327
7.
Left Derivations Characterized by Acting on Multilinear Polynomials, Communications in Algebra, 2011, 39, 6, 1979
8.
Additive mappings satisfying algebraic conditions in rings, Rendiconti del Circolo Matematico di Palermo (1952 -), 2014, 63, 2, 211
9.
Some Theorems for Sigma Prime Rings with Differential Identities on Sigma Ideals, ISRN Algebra, 2013, 2013, 1
10.
CHARACTERIZATIONS OF REAL HYPERSURFACES OF TYPE A IN A COMPLEX SPACE FORM, Bulletin of the Korean Mathematical Society, 2010, 47, 1, 1
References
1.
M. Ashraf, On left $({\theta},{\phi})$-derivations of prime rings, Arch. Math. (Brno) 41 (2005), no. 2, 157-166

2.
M. Ashraf, A. Ali, and S. Ali, On Lie ideals and generalized $({\theta},{\phi})$-derivations in prime rings, Comm. Algebra 32 (2004), no. 8, 2977-2985

3.
M. Ashraf and N. Rehman, On Jordan generalized derivations in rings, Math. J. Okayama Univ. 42 (2000), 7-9

4.
M. Ashraf and N. Rehman, On Lie ideals and Jordan left derivations of prime rings, Arch. Math. (Brno) 36 (2000), no. 3, 201-206

5.
M. Ashraf, N. Rehman, and S. Ali, On Jordan left derivations of Lie ideals in prime rings, Southeast Asian Bull. Math. 25 (2001), no. 3, 379-382

6.
M. Ashraf, N. Rehman, and S. Ali, On Lie ideals and Jordan generalized derivations of prime rings, Indian J. Pure Appl. Math. 34 (2003), no. 2, 291-294

7.
M. Bresar and J. Vukman, On left derivations and related mappings, Proc. Amer. Math. Soc. 110 (1990), no. 1, 7-16

8.
W. Cortes and C. Haetinger, On Jordan generalized higher derivations in rings, Turkish J. Math. 29 (2005), no. 1, 1-10

9.
Q. Deng, On Jordan left derivations, Math. J. Okayama Univ. 34 (1992), 145-147

10.
I. N. Herstein, Jordan derivations of prime rings, Proc. Amer. Math. Soc. 8 (1957), 1104-1110

11.
I. N. Herstein, Topics in Ring Theory, Univ. of Chicago Press, Chicago, 1969

12.
B. Hvala, Generalized derivations in rings, Comm. Algebra 26 (1998), no. 4, 1147-1166

13.
W. Jing and S. Lu, Generalized Jordan derivations on prime rings and standard operator algebras, Taiwanese J. Math. 7 (2003), no. 4, 605-613

14.
K. W. Jun and B. D. Kim, A note on Jordan left derivations, Bull. Korean Math. Soc. 33 (1996), no. 2, 221-228

15.
Y. S. Jung, Generalized Jordan triple higher derivations on prime rings, Indian J. Pure Appl. Math. 36 (2005), no. 9, 513-524

16.
E. C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957), 1093-1100

17.
J. Vukman, Jordan left derivations on semiprime rings, Math. J. Okayama Univ. 39 (1997), 1-6

18.
S. M. A. Zaidi, M. Ashraf, and S. Ali, On Jordan ideals and left $({\theta},{\theta})$-derivations in prime rings, Int. J. Math. Math. Sci. 2004 (2004), no. 37-40, 1957-1964

19.
B. Zalar, On centralizers of semiprime rings, Comment. Math. Univ. Carolin. 32 (1991), no. 4, 609-614