AN ENGEL CONDITION WITH GENERALIZED DERIVATIONS ON LIE IDEALS

AN ENGEL CONDITION WITH GENERALIZED DERIVATIONS ON LIE IDEALS

Let R be a prime ring, with extended centroid C, g a non-zero generalized derivation of R, L a non-central Lie ideal of R, k > 1 a fixed integer. If [g(u), u]k = 0, for all u, then either g(x) = ax, with a ∊ C or R satisfies the standard identity S₄. Moreover in the latter case either char(R) = 2...

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Bibliographic Details
Published in:Taiwanese journal of mathematics Vol. 12; no. 2; pp. 419 - 433
Main Authors: Argaç, N., Carini, L., De Filippis, V.
Format: Journal Article
Language:English
Published: Mathematical Society of the Republic of China (Taiwan) 01-04-2008
Subjects:
Algebra
Applied mathematics
Centroids
Differentials
Integers
Logical proofs
Mathematical rings
Mathematical theorems
Polynomials
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Summary:Let R be a prime ring, with extended centroid C, g a non-zero generalized derivation of R, L a non-central Lie ideal of R, k > 1 a fixed integer. If [g(u), u]k = 0, for all u, then either g(x) = ax, with a ∊ C or R satisfies the standard identity S₄. Moreover in the latter case either char(R) = 2 or char(R) ≠ 2 and g(x) = ax + xb, with a, b ∊ Q and a - b ∊ C. We also prove a more generalized version by replacing L with the set [I, I), where I is a right ideal of R.
ISSN:1027-5487
2224-6851
DOI:10.11650/twjm/1500574164