NOTES ON GENERALIZED DERIVATIONS ON LIE IDEALS IN PRIME RINGS

Title & Authors
NOTES ON GENERALIZED DERIVATIONS ON LIE IDEALS IN PRIME RINGS
Dhara, Basudeb; Filippis, Vincenzo De;

Abstract
Let R be a prime ring, H a generalized derivation of R and L a noncommutative Lie ideal of R. Suppose that $\small{u^sH(u)u^t}$
Keywords
prime ring;derivation;generalized derivation;extended centroid;Utumi quotient ring;
Language
English
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References
1.
K. I. Beidar, W. S. Martindale III, and A. V. Mikhalev, Rings with Generalized Identities, Monographs and Textbooks in Pure and Applied Mathematics, 196. Marcel Dekker, Inc., New York, 1996

2.
C.-M. Chang and Y.-C. Lin, Derivations on one-sided ideals of prime rings, Tamsui Oxf. J. Math. Sci. 17 (2001), no. 2, 139–145

3.
C. L. Chuang, GPIs having coefficients in Utumi quotient rings, Proc. Amer. Math. Soc. 103 (1988), no. 3, 723–728

4.
B. Dhara and R. K. Sharma, Derivations with annihilator conditions in prime rings, Publ. Math. Debrecen 71 (2007), no. 1-2, 11–20

5.
T. S. Erickson, W. S. Martindale III, and J. M. Osborn, Prime nonassociative algebras, Pacific J. Math. 60 (1975), no. 1, 49–63

6.
C. Faith and Y. Utumi, On a new proof of Litoff's theorem, Acta Math. Acad. Sci. Hungar 14 (1963), 369–371

7.
I. N. Herstein, Topics in Ring Theory, Univ. of Chicago Press, Chicago, IL, 1969

8.
B. Hvala, Generalized derivations in rings, Comm. Algebra 26 (1998), no. 4, 1147–1166

9.
N. Jacobson, Structure of Rings, Amer. Math. Soc. Colloq. Pub., 37, Amer. Math. Soc., Providence, RI, 1964

10.
V. K. Kharchenko, Differential identities of prime rings, Algebra i Logika 17 (1978), no. 2, 220–238, 242–243

11.
C. Lanski, Differential identities, Lie ideals, and Posner's theorems, Pacific J. Math. 134 (1988), no. 2, 275–297

12.
C. Lanski, An Engel condition with derivation, Proc. Amer. Math. Soc. 118 (1993), no. 3, 731–734

13.
T. K. Lee, Generalized derivations of left faithful rings, Comm. Algebra 27 (1999), no. 8, 4057–4073

14.
T. K. Lee, Semiprime rings with differential identities, Bull. Inst. Math. Acad. Sinica 20 (1992), no. 1, 27–38

15.
W. S. Martindale III, Prime rings satisfying a generalized polynomial identity, J. Algebra 12 (1969), 576–584