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GENERALIZED DERIVATIONS AND DERIVATIONS OF RINGS AND BANACH ALGEBRAS
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  • Journal title : Honam Mathematical Journal
  • Volume 35, Issue 4,  2013, pp.625-637
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2013.35.4.625
 Title & Authors
GENERALIZED DERIVATIONS AND DERIVATIONS OF RINGS AND BANACH ALGEBRAS
Jung, Yong-Soo;
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 Abstract
We investigate anti-centralizing and skew-centralizing mappings involving generalized derivations and derivations on prime and semiprime rings. We also obtain some range inclusion results for generalized linear derivations and linear derivations on Banach algebras by applying the algebraic techniques. Some results in this note are to improve the ones in [22].
 Keywords
Generalized derivations;derivations;prime rings;semiprime rings;Banach algebras;
 Language
English
 Cited by
 References
1.
K.I. Beidar, Rings of quotients of semiprime rings, Vestnik Moskov. Univ. Ser I Mat. Meh. (Engl. Transl. Moscow Univ. Math. Bull.) 33 (1978), 36-42.

2.
M. Bresar, On skew-commuting mappings of rings, Bull. Austral. Math. Soc. 47 (1993), 291-296. crossref(new window)

3.
M. Bresar, On the distance of the compositions of two derivations to the generalized derivations, Glasgow Math. J. 33 (1991), 89-93. crossref(new window)

4.
M. Bresar and J. Vukman, Derivations of noncommutative Banach algebras, Arch. Math. 59 (1992), 363-370. crossref(new window)

5.
L.-O. Chung and J. Luh, Semiprime rings with nilpotent derivations, Canad. Math. Bull. 24 (1981), 415-421. crossref(new window)

6.
J. Cusack, Automatic continuity and topologically simple radical Banach algebras, J. London Math. Soc. 16(2) (1977), 493-500.

7.
Q. Deng and H. E. Bell, On derivations and commutativity in semiprime rings, Comm. Algebra 23 (1995), 3705-3713. crossref(new window)

8.
R.V. Garimella, Continuity of derivations on some semiprime Banach algebras, Proc. Amer. Math. Soc. 66(22) (1987), 289-292.

9.
B. Hvala, Generalized derivations in rings, Comm. Algebra 26(4) (1998), 1147-1166. crossref(new window)

10.
T.-K. Lee, Semiprime rings with dierential identities, Bull. Inst. Math. Acad. Sinica 20 (1992), 27-38.

11.
T.-K. Lee, Generalized derivations of left faithful rings, Comm. Algebra 27(8) (1999), 4057-4073. crossref(new window)

12.
M. Mathieu and V. Runde, Derivations mapping into the radical II, Bull. London Math. Soc. 24 (1992), 485-487. crossref(new window)

13.
E. Posner, Derivations in Prime rings, Proc. Amer. Math. Soc. 8 (1957), 1093-1102.

14.
M. A. Quadri, M. Shadab Khan and N. Rehman, Generalized derivations and commutativity of prime rings, Indian J. pure appl. Math. 34(9) (2003), 1393-1396.

15.
C.E. Rickart. General theory of Banach algebra, Van Nostrand, Princeton (1950).

16.
A. M. Sinclair, Continuous derivations on Banach algebras, Proc. Amer. Math. Soc. 20 (1969), 166-170.

17.
A. M. Sinclair, Automatic continuity of linear operators, London Math. Soc. Lecture Note Ser. 21, 1976.

18.
I.M. Singer and J. Wermer, Derivations on commutative normed algebras, Math. Ann. 129 (1955), 435-460.

19.
M.P. Thomas, The image of a derivation is contained in the radical, Annals of Math. 128 (1988), 435-460. crossref(new window)

20.
M.P. Thomas, Primitive ideals and derivations on noncommutative Banach algebras, Pacic. J. Math.159 (1993), 139-152. crossref(new window)

21.
J. Vukman, Identities with derivations on rings and Banach algebras, Glas. Mat. Ser. III, 40 (2005), 189-199. crossref(new window)

22.
F. Wei and Z. Xiao, Pair of (generalized-)derivations on rings and Banach algebras, Bull. Korean Math. Soc. 46(5) (2009), 857-866. crossref(new window)