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Abstrakty
We give a generalization of Vukman's theorem concerning a pair of derivations on rings. Then applying this purely algebraic result we obtain several range inclusion results of pair of derivations on Banach algebras.
Wydawca
Czasopismo
Rocznik
Tom
Strony
297--308
Opis fizyczny
Bibliogr. 25 poz.
Twórcy
autor
autor
- Department of Mathematics Beijing Institute of Technology, Beijing, 100081, China, daoshu@bit.edu.cn
Bibliografia
- [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. Brešar, Centralizing mappings and derivations in prime rings, J. Algebra 156 (1993), 385-394.
- [3] M. Brešar and J. Vukman, Derivations on noncommutative Banach algebras, Arch. Math.(Basel), 59 (1992), 363-370.
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- [5] M. A. Chaudhry and A. B. Thaheem, On (α, β)-derivations of semiprime rings, Demonstratio Math. XXXVI (2003), 283-287.
- [6] M. A. Chaudhry and A. B. Thaheem, On (α, β)-derivations of semiprime rings. II, Demonstratio Math. XXXVII (2004), 793-802.
- [7] M. A. Chaudhry and A. B. Thaheem, On a pair of derivations of semiprime rings, Int. J. Math. Math. Sci. 39 (2004), 2097-2112.
- [8] L. O. Chung and J. Luh, Semiprime rings with nilpotent derivations, Canad. Math. Bull. 24 (1981), 415-421.
- [9] J. Cusack, Automatic continuity and topologically simple radical Banach algebras, J. London Math. Soc. 16 (1977), 493-500,
- [10] I. N. Herstein, Jordan derivations on prime rings, Proc. Amer. Math. Soc. 8 (1957), 1104-1110.
- [11] B. E. Johnson and A. M. Sinclair, Continuity of derivations and a problem of Kaplansky, Amer J. Math. 90 (1968), 1067-1073.
- [12] M. Mathieu and V. Runde, Derivations mapping into the radical, II, Bull. London Math. Soc. 24 (1992), 485-487.
- [13] M. Mathieu, Where to find the image of a derivation, Banach Center Publ. 30 (1994), 237-249.
- [14] K. H. Park, Y. S. Jung and J. H. Bae, Derivations in Banach algebras, Int. J. Math. Math. Sci. 29:10 (2002), 579-583.
- [15] E. C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957), 1093-1100.
- [16] A. M. Sinclair, Jordan homomorphisms and derivations on semisimple Banach algebras, Proc. Amer. Math. Soc. 24 (1970), 209-214.
- [17] A. M. Sinclair, Automatic Continuity of Linear Operators, London Mathematical Society Lecture Note Series V. 21, Cambridge University Press, Cambridge, 1976.
- [18] I. M. Singer and J. Wermer, Derivations on commutative normed algebras, Math. Ann. 129 (1955), 260-264.
- [19] M. P. Thomas, The image of a derivation is contained in the radical, Ann. Math. 128 (1988), 435-460.
- [20] M. P. Thomas, Primitive ideals and derivations on noncommutative Banach algebras, Pacific. J. Math., 159 (1993), 139-152.
- [21] A. R. Villena, Automatic continuity in associative and nonassociative context, Irish Math. Soc. Bull., 46 (2001), 43-76.
- [22] J. Vukman, Identities with derivations on rings and Banach algebras, Glas. Mat. Ser. III. 40 (2005), 189-199.
- [23] J. Vukman, On α-derivations of prime and semiprime rings, Demonstratio Math. XXXVIII (2005), 283-290.
- [24] J. Vukman and I. Kosi-Ulbl, On dependent elements in rings, Int. J. Math. Math. Sci. 54 (2004), 2895-2906.
- [25] J. Vukman and I. Kosi-Ulbl, On some equations related to derivations in rings and Banach algebras, Demonstratio Math. XXXIX (2006), 61-66.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA3-0048-0006