Generalized Derivations on (Semi-)Prime Rings and Noncommutative Banach Algebras
Rendiconti del Seminario Matematico della Università di Padova, Tome 122 (2009), pp. 171-190. 
@article{RSMUP_2009__122__171_0,
     author = {Wei, Feng and Xiao, Zhankui},
     title = {Generalized {Derivations} on {(Semi-)Prime} {Rings} and {Noncommutative} {Banach} {Algebras}},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {171--190},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {122},
     year = {2009},
     mrnumber = {2582836},
     zbl = {1195.16041},
     language = {en},
     url = {http://www.numdam.org/item/RSMUP_2009__122__171_0/}
}
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Wei, Feng; Xiao, Zhankui. Generalized Derivations on (Semi-)Prime Rings and Noncommutative Banach Algebras. Rendiconti del Seminario Matematico della Università di Padova, Tome 122 (2009), pp. 171-190. http://www.numdam.org/item/RSMUP_2009__122__171_0/

[1] E. Albas - N. Argac, Generalized derivations of prime rings, Algebra Colloq., 11 (2004), pp. 399-410. | MR | Zbl

[2] K. I. Beidar, Rings of quotients of semiprime rings, Vestnik Moskov. Univ. Ser I Mat. Meh. (Engl. Transl. Moscow Univ. Math. Bull.), 33 (1978), pp. 36-42. | MR | Zbl

[3] M. Bresïar, Jordan mappings of semiprime rings, J. Algebra, 127 (1989), pp. 218-228. | MR | Zbl

[4] D. S. Bridges - J. Bergen, On the derivation of xn in a ring, Proc. Amer. Math. Soc., 90 (1984), pp. 25-29. | MR | Zbl

[5] L. O. Chung - J. Luh, Semiprime rings with nilpotent derivations, Canad. Math. Bull., 24 (1981), pp. 415-421. | MR | Zbl

[6] J. Cusack, Jordan derivations on rings, Proc. Amer. Math. Soc., 53 (1975), pp. 321-324. | MR | Zbl

[7] V. De Filippis, An Engel condition with generalized derivations on multilinear polynomials, Israel J. Math., 162 (2007), pp. 93-108. | MR | Zbl

[8] V. De Filippis, Posner's second theorem and an annihilator condition with generalized derivations, Turkish J. Math., 32 (2008), pp. 197-211. | MR | Zbl

[9] V. De Filippis, Generalized derivations in prime rings and noncommutative Banach algebras, Bull. Korean Math. Soc., 45 (2008), pp. 621-629. | MR | Zbl

[10] V. De Filippis - H. G. Inceboz, Generalized derivations with power central values on multilinear polynomials on right ideals, Rend. Sem. Mat. Univ. Padova, 120 (2008), pp. 59-71. | Numdam | MR

[11] V. De Filippis - M. S. Tammam El-Sayiad, A note on Posner's theorem with generalized derivations on Lie ideals, Rend. Sem. Mat. Univ. Padova, 122 (2009), pp. 55-64.

[12] I. N. Herstein, Jordan derivations of prime rings, Proc. Amer. Math. Soc., 8 (1957), pp. 1104-1110. | MR | Zbl

[13] B. E. Johnson - A. M. Sinclair, Continuity of derivations and a problem of Kaplansky, Amer J. Math., 90 (1968), pp. 1067-1073. | MR | Zbl

[14] K. -W. JUN - H. - M. KIM, Derivations on prime rings and Banach algebras, Bull. Korean Math. Soc., 38 (2001), pp. 709-718. | MR | Zbl

[15] C. Lanski, An Engel condition with derivation, Proc. Amer. Math. Soc., 118 (1993), pp. 731-734. | MR | Zbl

[16] T. K. Lee, Semiprime rings with differential identities, Bull. Inst. Math. Acad. Sinica, 20 (1992), pp. 27-38. | Zbl

[17] M. Mathieu - V. Runde, Derivations mapping into the radical, II, Bull. London Math. Soc., 24 (1992), pp. 485-487. | Zbl

[18] E. Posner, Derivations in prime rings, Proc. Amer. Math. Soc., 8 (1957), pp. 1093-1100. | Zbl

[19] A. M. Sinclair, Jordan homomorphisms and derivations on semisimple Banach algebras, Proc. Amer. Math. Soc., 24 (1970), pp. 209-214. | Zbl

[20] A. M. Sinclair, Automatic Continuity of Linear Operators, London Mathematical Society Lecture Note Series, V. 21, Cambridge University Press (Cambridge, 1976). | MR | Zbl

[21] I. M. Singer - J. Wermer, Derivations on commutative normed algebras, Math. Ann., 129 (1955), pp. 260-264. | MR | Zbl

[22] M. P. Thomas, The image of a derivation is contained in the radical, Ann. Math., 128 (1988), pp. 435-460. | MR | Zbl

[23] M. P. Thomas, Primitive ideals and derivations on noncommutative Banach algebras, Pacific. J. Math., 159 (1993), pp. 139-152. | MR | Zbl

[24] J. Vukman, Identities with derivations on rings and Banach algebras, Glasnik Matematicki, 40 (2005), pp. 189-199. | MR | Zbl

[25] J. Vukman - I. Kosi-Ulbl, A note on derivations in semiprime rings, Int. J. Math. Math. Sci., 20 (2005), pp. 3347-3350. | MR | Zbl

[26] F. Wei, Generalized derivations with nilpotent values on semiprime rings, Acta Math. Sinica, 20 (2004), pp. 453-462. | MR | Zbl

[27] F. Wei - Z. -K. Xiao, Generalized Jordan (triple-)derivations and pairs of Jordan derivations on semiprime rings, Demonstratio Math., in press. | Zbl

[28] F. Wei - Z. -K. Xiao, Pair of (Generalized-) Derivations on Rings and Banach Algebras, Bull. Korean Math. Soc., 46 (2009), pp. 857-866. | MR