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http://dx.doi.org/10.5831/HMJ.2013.35.4.625

GENERALIZED DERIVATIONS AND DERIVATIONS OF RINGS AND BANACH ALGEBRAS  

Jung, Yong-Soo (Department of Mathematics, Sun Moon University)
Publication Information
Honam Mathematical Journal / v.35, no.4, 2013 , pp. 625-637 More about this Journal
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;
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Times Cited By KSCI : 1  (Citation Analysis)
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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.   DOI
3 M. Bresar, On the distance of the compositions of two derivations to the generalized derivations, Glasgow Math. J. 33 (1991), 89-93.   DOI
4 M. Bresar and J. Vukman, Derivations of noncommutative Banach algebras, Arch. Math. 59 (1992), 363-370.   DOI
5 L.-O. Chung and J. Luh, Semiprime rings with nilpotent derivations, Canad. Math. Bull. 24 (1981), 415-421.   DOI
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.   DOI   ScienceOn
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.   DOI   ScienceOn
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.   DOI   ScienceOn
12 M. Mathieu and V. Runde, Derivations mapping into the radical II, Bull. London Math. Soc. 24 (1992), 485-487.   DOI
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.   DOI   ScienceOn
20 M.P. Thomas, Primitive ideals and derivations on noncommutative Banach algebras, Pacic. J. Math.159 (1993), 139-152.   DOI
21 J. Vukman, Identities with derivations on rings and Banach algebras, Glas. Mat. Ser. III, 40 (2005), 189-199.   DOI
22 F. Wei and Z. Xiao, Pair of (generalized-)derivations on rings and Banach algebras, Bull. Korean Math. Soc. 46(5) (2009), 857-866.   과학기술학회마을   DOI   ScienceOn