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Kragujevac Journal of Mathematics
2017, vol. 41, br. 1, str. 105-120
jezik rada: engleski
vrsta rada: neklasifikovan
doi:10.5937/KgJMath1701105R


On generalized derivation in rings and Banach algebras
(naslov ne postoji na srpskom)
Department of Mathematics, Aligarh Muslim University, Aligarh, India

e-adresa: arifraza03@gmail.com, rehman100@gmail.com

Sažetak

(ne postoji na srpskom)
Let R be a prime ring, F be a generalized derivation associated with a derivation d of R and m, n be the fixed positive integers. In this paper we study the case when one of the following holds: (i) F(x) ◦m F(y) = (x ◦ y)n, (ii) F(x)◦md(y) = d(x◦y)n for all x, y in some appropriate subset of R. We also examine the case where R is a semiprime ring. Finally, as an application we obtain some range inclusion results of continuous or spectrally bounded generalized derivations on non-commutative Banach algebras.

Ključne reči

prime and semiprime rings; generalized derivation; generalized polynomial identity (GPI); ideal

Reference

Ali, S., Ashraf, M., Khan, M.S., Vukman, J. (2014) Commutativity of rings involving additive mappings. Quaestiones Mathematicae, 37(2): 215-229
Argaç, N., Inceboz, H.G. (2009) Derivation of prime and semiprime rings. J. Korean Math. Soc., 997-1005; 46
Ashraf, M., Rehman, N. (2002) On Commutativity of Rings With Derivations. Results in Mathematics, 42(1-2): 3-8
Beidar, K.I., W.S.M.III,, Mikhalev, A.V. (1996) Rings with Generalized Identities. u: Pure and Applied Mathematics, New York: Marcel Dekker, 196
Bell, H. E., Daif, M. N. (1995) On derivations and commutativity in prime rings. Acta Mathematica Hungarica, 66(4): 337-343
Bell, H.E., Rehman, N. (2007) Generalized derivations with commutativity and anti-commutativity conditions. Math. J. Okayama Univ., 139-147; 49
Bell, H.E., Daif, M.N. (1994) On commutativity and strong commutativity-preserving maps. Bulletin canadien de mathématiques, 37(4): 443-447
Bresar, M., Mathieu, M. (1995) Derivations Mapping into the Radical III. Journal of Functional Analysis, 133(1): 21-29
Bresar, M. (1991) On the distance of the composition of two derivations to the generalized derivations. Glasgow Mathematical Journal, 33(01): 89
Carini, L., de Filippis, V. (2000) Commutators with power central values on a Lie ideal. Pacific Journal of Mathematics, 193(2): 269-278
Chuang, C.L. (1994) Hypercentral Derivations. Journal of Algebra, 166(1): 34-71
Chuang, C. (1988) GPIs having coefficients in Utumi quotient rings. Proceedings of the American Mathematical Society, 103(3): 723-723
Daif, M.N., Bell, H.E. (1992) Remarks on derivations on semiprime rings. International Journal of Mathematics and Mathematical Sciences, 15(1): 205-206
de Filippis, V., Huang, S. (2011) Generalized derivations on semiprime rings. Bulletin of the Korean Mathematical Society, 48(6): 1253-1259
Erickson, T., Martindale, W., Osborn, J. (1975) Prime nonassociative algebras. Pacific Journal of Mathematics, 60(1): 49-63
Herstein, I. (1979) Center-like elements in prime rings. Journal of Algebra, 60(2): 567-574
Huang, S. (2012) ON GENERALIZED DERIVATIONS OF PRIME AND SEMIPRIME RINGS. Taiwanese Journal of Mathematics, 16(2): 771-776
Jacobson, N. (1956) Structure of Rings. Amer. Math. Soc., Colloquium Publications 37; VII, Provindence, RI
Johnson, B. E., Sinclair, A. M. (1968) Continuity of Derivations and a Problem of Kaplansky. American Journal of Mathematics, 90(4): 1067
Kharchenko, V. K. (1978) Differential identities of prime rings. Algebra and Logic, 17(2): 155-168
Lanski, C. (1993) An Engel condition with derivation. Proceedings of the American Mathematical Society, 118(3): 731-731
Lee, T.K. (1992) Semiprime rings with differential identities. Bull. Inst. Math. Acad. Sinica, 27-38; 20
Lee, T. (1999) Generalized derivations of left faithful rings. Communications in Algebra, 27(8): 4057-4073
Mathieu, M., Murphy, G. J. (1991) Derivations mapping into the radical. Archiv der Mathematik, 57(5): 469-474
Mayne, J.H. (1984) Centralizing mappings of prime rings. Canad. Math. Bull, 27(1), 122-126
Posner, E.C. (1957) Derivations in prime rings. Proceedings of the American Mathematical Society, 8(6): 1093-1093
Raza, M.A., Rehman, N.U. (2016) On prime and semiprime rings with generalized derivations and non-commutative Banach algebras. Proceedings - Mathematical Sciences, 126(3): 389-398
Rehman, N.ur, Arif, R.M., Bano, T. (2016) On commutativity of rings with generalized derivations. Journal of the Egyptian Mathematical Society, 24(2): 151-155
Rehman, N.ur, Raza, M.A., Huang, S. (2015) On generalized derivations in prime ring with skew-commutativity conditions. Rendiconti del Circolo Matematico di Palermo, 64(2): 251-259
Shuliang, H. (2007) Generalized Derivations of Prime Rings. International Journal of Mathematics and Mathematical Sciences, 2007: 1-6
Sinclair, A. M. (1969) Continuous derivations on Banach algebras. Proceedings of the American Mathematical Society, 20(1): 166-166
Singer, I. M., Wermer, J. (1955) Derivations on commutative normed algebras. Mathematische Annalen, 129(1): 260-264
Thomas, M.P. (1988) The Image of a Derivation is Contained in the Radical. Annals of Mathematics, 128(3): 435
W.S.M.III (1969) Prime rings satisfying a generalized polynomial identity. J. Algebra, 576-584; 12
Xu, X.W. (2006) The power values properties of generalized derivations. Changchun: Jilin University, Doctoral Thesis