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Derivations with Power Values on Lie Ideals in Rings and Banach Algebras
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  • Journal title : Kyungpook mathematical journal
  • Volume 56, Issue 2,  2016, pp.397-408
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2016.56.2.397
 Title & Authors
Derivations with Power Values on Lie Ideals in Rings and Banach Algebras
Rehman, Nadeem ur; Muthana, Najat Mohammed; Raza, Mohd Arif;
  PDF(new window)
 Abstract
Let R be a 2-torsion free prime ring with center Z, U be the Utumi quotient ring, Q be the Martindale quotient ring of R, d be a derivation of R and L be a Lie ideal of R. If $d(uv)^n
 Keywords
Prime and semiprime rings;Derivations;Martindale ring of quotients;Banach algebras;Radical;
 Language
English
 Cited by
 References
1.
A. Ali, N. Rehman and A. Shakir, On Lie ideals with derivations as homomorphisms and anti-homomorphisms, Acta Math. Hungar., 101(1-2)(2003), 79-82. crossref(new window)

2.
K. I. Beidar, W. S. Martindale III and A. V. Mikhalev, Rings with Generalized Identities, Pure and Applied Mathematics, Marcel Dekker 196, New York, 1996.

3.
H. E. Bell and L. C. Kappe, Rings in which derivations satisfy certain algebraic conditions, Acta Math. Hungar., 53(1989), 339-346. crossref(new window)

4.
J. Bergen and L. Carini, A note on derivations with power central values on a Lie ideal, Pacific J. Math., 132(2)(1988), 209-213. crossref(new window)

5.
C. L. Chuang, GPIs having coefficients in Utumi quotient rings, Proc. Amer. Math. Soc., 103(1988), 723-728. crossref(new window)

6.
C. L. Chuang, Hypercentral derivations, J. Algebra, 166(1)(1994), 34-71. crossref(new window)

7.
V. De Filippis, Generalized derivations in prime rings and noncommutative Banach algebras, Bull. Korean Math. Soc., 45(2008), 621-629.

8.
T. S. Erickson, W. S. Martindale III and J. M. Osborn, Prime nonassociative algebras, Pacific J. Math., 60(1)(1975), 49-63. crossref(new window)

9.
I. N. Herstein, Topics in Ring Theory, Univ. of Chicago Press, 1969.

10.
I. N. Herstein, Derivations of prime rings having power central values, Algebraist's Homage. Contemporary Mathematics. Vol. 13, Amer. Math. Soc., Providence, Rhode Island, 1982.

11.
N. Jacobson, Structure of Rings, Colloquium Publications Vol. XXXVII, Amer. Math. Soc., 190 Hope street, Provindence, R. I., 1956.

12.
B. E. Johnson and A. M. Sinclair, Continuity of derivations and a problem of Kaplansky, Amer. J. Math., 90(1968), 1067-1073. crossref(new window)

13.
V. K. Kharchenko, Differential identities of prime rings, Algebra Logic, 17(2)(1979), 155-168.

14.
C. Lanski, An Engel condition with derivation, Proc. Amer. Math. Soc., 118(1993), 731-734. crossref(new window)

15.
T. K. Lee, Semiprime rings with differential identities, Bull. Inst. Math., Acad. Sin., 20(1)(1992), 27-38.

16.
P. H. Lee and T. L. Wong, Derivations cocentralizing Lie ideals, Bull. Inst. Math. Acad. Sin., 23(1)(1995), 1-5.

17.
W. S. Martindale III, Prime rings satisfying a generalized polynomial identity, J. Algebra, 12(4)(1969), 576-584. crossref(new window)

18.
M. Mathieu and G. J. Murphy, Derivations mapping into the radical, Arch. Math., 57(1991), 469-474. crossref(new window)

19.
M. Mathieu and V. Runde, Derivations mapping into the radical II, Bull. Lond. Math. Soc., 24(1992), 485-487. crossref(new window)

20.
K. H. Park, On derivations in noncommutative semiprime rings and Banach algebras, Bull. Korean Math. Soc., 42 (2005), 671-678. crossref(new window)

21.
E. C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc., 8(1958), 1093-1100.

22.
A. M. Sinclair, Continuous derivations on Banach algebras, Proc. Amer. Math. Soc., 20(1969), 166-170. crossref(new window)

23.
I. M. Singer and J. Wermer, Derivations on commutative normed algebras, Math. Ann., 129(1955), 260-264. crossref(new window)

24.
M. P. Thomas, The image of a derivation is contained in the radical, Ann. Math., 128(2)(1988), 435-460. crossref(new window)

25.
Y. Wang and H. You, Derivations as homomorphisms or anti-homomorphisms on Lie ideals, Acta Math. Sinica., 23(6)(2007), 1149-1152. crossref(new window)