Yiqiu DU, Yu Wang A Result On Generalized Derivat STATISTICS

A Result On Generalized Derivations in Prime Rings ABSTRACT | FULL TEXT

Anahtar Kelimeler:

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A Result On Generalized Derivations in Prime Rings ABSTRACT | FULL TEXT

Let R be a prime ring, H a generalized derivation of R, L a noncentralLie ideal of R, and 0 = a ∈ R. Suppose that aus (H(u))n u t = 0 forall u ∈ L, where s, t ≥ 0 and n > 0 are fixed integers. If s = 0, thenH(x) = bx for all x ∈ R, where b ∈ U , the right Utumi quotient ringof R, with ab = 0 unless R satisfies s, the standard identity in fourvariables. If s > 0, then H = 0 unless R satisfies s.

Keywords:

prime ring, derivation, generalized derivation, extended centroid rightUtumi quotient ring.,

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Albas, B., Argac, N. and Fillippis, V. D. Generalized derivations with Engel conditions on one-sided ideals, Comm. Algebra 36, 2063-2071, 2008.
Albert A. A. and Muckenhoupt, B. On matrices of trace zero Michigan J. Math. 1, 1-3, 1957.
Beidar, K. I., Martindale W. S. and Mikhalev, A. V. Rings with Generalized Identities, Marcel Dekker, New York-Basel-Hong Kong, 1996.
Chuang, C. L. GPIs having coefficients in Utumi quotient rings, Proc. Amer. Math. Soc. 103, 723-728, 1988.
Dhara, B. and De Filippis, V. Notes on generalized derivations on Lie ideals in prime rings, Bull. Korean Math. Soc. 46 (3), 599-605, 2009.
Dhara, B and Sharma, R. K. Derivations with annihilator conditions in prime rings, Publ. Math. Debrecen 71 (1), 11-20, 2007.
Erickson, T. S., Martindale, W S. and Osborn, J. M. Prime nonassociative algebras, Pacific J. Math. 60 (1), 49-63, 1975.
Faith, C. and Utumi, Y. On a new proof of Litoff ’s theorem, Acta Math. Acad. Sci. Hung. 14, 369-371, 1963.
De Filippis, V. An Engel condition with generalized derivations on multilinear polynomials, Israel J. Math. 162, 93-108, 2007.
De Filippis, V. Posner’s second theorem and an annihilator condition with generalized derivations, Turk J. Math. 32, 197-211, 2008.
De Filippis, V. Generalized derivations in prime rings and noncommutative Banach algebras, Bull. Korean Math. Soc. 45, 621-629, 2008.
Hvala, B. Generalized derivations in rings, Comm. Algebra 26, 1147-1166, 1998. Jacobson, N. Structure of Rings, Amer. Math. Soc. Colloq. Pub., 37, Amer. Math. Soc., Providence, RI, 1964.
Kharchenko, V. K. Differential identities of prime rings, Algebra and Logic 17 155-168, 19 Lanski, C. and Montgomery, S. Lie structure of prime rings of characteristic 2, Pacific J. Math. 42, 117-136, 1972.
Lee, T. K. Generalized derivations of left faithful rings, Comm. Algebra 27, 4057-4073, 19
Lee, T. K. and Lin, J. S. A result on derivations, Proc. Amer. Math. Soc. 124, 16871691, 1996.
Lee, T. K. Lee and Shiue, W. K. Identities with generalized derivations, Comm. Algebra 29, 4437-4450, 2001.
Lin, J. S. and Liu, C. K. Generalized derivations with invertible or nilpotent on multilinear polynomials values, Comm. Algebra 34, 633-640, 2006.
Martindale 3rd, W. S. Prime rings satisfying a generalized polynomial identity, J. Algebra 12, 576-584, 1969.
Wang, Y. Generalized derivations with power-central values on multilinear polynomials, Algebra Colloq. 13, 405-410, 2006.
Wang, Y. Annihilator conditions with generalized derivations in prime rings, Bull. Korean Math. Soc. 48, 917-922, 2011.