Generalized Derivations on (Semi-)Prime Rings and Noncommutative Banach Algebras
Rendiconti del Seminario Matematico della Università di Padova (2009)
- Volume: 122, page 171-190
- ISSN: 0041-8994
Access Full Article
topHow to cite
topWei, Feng, and Xiao, Zhankui. "Generalized Derivations on (Semi-)Prime Rings and Noncommutative Banach Algebras." Rendiconti del Seminario Matematico della Università di Padova 122 (2009): 171-190. <http://eudml.org/doc/108769>.
@article{Wei2009,
author = {Wei, Feng, Xiao, Zhankui},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {semiprime rings; additive maps; generalized derivations; generalized Jordan derivations; prime rings; left multiplications; central identities; Banach algebras},
language = {eng},
pages = {171-190},
publisher = {Seminario Matematico of the University of Padua},
title = {Generalized Derivations on (Semi-)Prime Rings and Noncommutative Banach Algebras},
url = {http://eudml.org/doc/108769},
volume = {122},
year = {2009},
}
TY - JOUR
AU - Wei, Feng
AU - Xiao, Zhankui
TI - Generalized Derivations on (Semi-)Prime Rings and Noncommutative Banach Algebras
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2009
PB - Seminario Matematico of the University of Padua
VL - 122
SP - 171
EP - 190
LA - eng
KW - semiprime rings; additive maps; generalized derivations; generalized Jordan derivations; prime rings; left multiplications; central identities; Banach algebras
UR - http://eudml.org/doc/108769
ER -
References
top- [1] E. ALBAS - N. ARGAC, Generalized derivations of prime rings, Algebra Colloq., 11 (2004), pp. 399-410. Zbl1074.16022MR2081197
- [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. Zbl0403.16003MR516019
- [3] M. BRESÏAR, Jordan mappings of semiprime rings, J. Algebra, 127 (1989), pp. 218-228. Zbl0691.16040MR1029414
- [4] D. S. BRIDGES - J. BERGEN, On the derivation of xn in a ring, Proc. Amer. Math. Soc., 90 (1984), pp. 25-29. Zbl0528.16021MR722408
- [5] L. O. CHUNG - J. LUH, Semiprime rings with nilpotent derivations, Canad. Math. Bull., 24 (1981), pp. 415-421. Zbl0477.16016MR644530
- [6] J. CUSACK, Jordan derivations on rings, Proc. Amer. Math. Soc., 53 (1975), pp. 321-324. Zbl0327.16020MR399182
- [7] V. DE FILIPPIS, An Engel condition with generalized derivations on multilinear polynomials, Israel J. Math., 162 (2007), pp. 93-108. Zbl1142.16023MR2365855
- [8] V. DE FILIPPIS, Posner's second theorem and an annihilator condition with generalized derivations, Turkish J. Math., 32 (2008), pp. 197-211. Zbl1152.16025MR2423389
- [9] V. DE FILIPPIS, Generalized derivations in prime rings and noncommutative Banach algebras, Bull. Korean Math. Soc., 45 (2008), pp. 621-629. Zbl1168.16020MR2463137
- [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. Zbl1228.16039MR2492650
- [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. Zbl1183.16035
- [12] I. N. HERSTEIN, Jordan derivations of prime rings, Proc. Amer. Math. Soc., 8 (1957), pp. 1104-1110. Zbl0216.07202MR95864
- [13] B. E. JOHNSON - A. M. SINCLAIR, Continuity of derivations and a problem of Kaplansky, Amer J. Math., 90 (1968), pp. 1067-1073. Zbl0179.18103MR239419
- [14] K. -W. JUN - H. - M. KIM, Derivations on prime rings and Banach algebras, Bull. Korean Math. Soc., 38 (2001), pp. 709-718. Zbl1029.47022MR1865829
- [15] C. LANSKI, An Engel condition with derivation, Proc. Amer. Math. Soc., 118 (1993), pp. 731-734. Zbl0821.16037MR1132851
- [16] T. K. LEE, Semiprime rings with differential identities, Bull. Inst. Math. Acad. Sinica, 20 (1992), pp. 27-38. Zbl0769.16017
- [17] M. MATHIEU - V. RUNDE, Derivations mapping into the radical, II, Bull. London Math. Soc., 24 (1992), pp. 485-487. Zbl0733.46023
- [18] E. POSNER, Derivations in prime rings, Proc. Amer. Math. Soc., 8 (1957), pp. 1093-1100. Zbl0082.03003
- [19] A. M. SINCLAIR, Jordan homomorphisms and derivations on semisimple Banach algebras, Proc. Amer. Math. Soc., 24 (1970), pp. 209-214. Zbl0175.44001
- [20] A. M. SINCLAIR, Automatic Continuity of Linear Operators, London Mathematical Society Lecture Note Series, V. 21, Cambridge University Press (Cambridge, 1976). Zbl0313.47029MR487371
- [21] I. M. SINGER - J. WERMER, Derivations on commutative normed algebras, Math. Ann., 129 (1955), pp. 260-264. Zbl0067.35101MR70061
- [22] M. P. THOMAS, The image of a derivation is contained in the radical, Ann. Math., 128 (1988), pp. 435-460. Zbl0681.47016MR970607
- [23] M. P. THOMAS, Primitive ideals and derivations on noncommutative Banach algebras, Pacific. J. Math., 159 (1993), pp. 139-152. Zbl0739.47014MR1211389
- [24] J. VUKMAN, Identities with derivations on rings and Banach algebras, Glasnik Matematicki, 40 (2005), pp. 189-199. Zbl1093.16033MR2189469
- [25] J. VUKMAN - I. KOSI-ULBL, A note on derivations in semiprime rings, Int. J. Math. Math. Sci., 20 (2005), pp. 3347-3350. Zbl1095.16018MR2208058
- [26] F. WEI, Generalized derivations with nilpotent values on semiprime rings, Acta Math. Sinica, 20 (2004), pp. 453-462. Zbl1064.16036MR2084708
- [27] F. WEI - Z. -K. XIAO, Generalized Jordan (triple-)derivations and pairs of Jordan derivations on semiprime rings, Demonstratio Math., in press. Zbl1139.16023
- [28] F. WEI - Z. -K. XIAO, Pair of (Generalized-) Derivations on Rings and Banach Algebras, Bull. Korean Math. Soc., 46 (2009), pp. 857-866. Zbl1185.16046MR2554280
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.