Annihilator condition of a pair of derivations in prime and semiprime rings

Basudeb Dhara (), Nurcan Argaç () and Krishna Gopal Pradhan ()
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Basudeb Dhara: Belda College
Nurcan Argaç: Ege University
Krishna Gopal Pradhan: Belda College

Indian Journal of Pure and Applied Mathematics, 2016, vol. 47, issue 1, 111-124

Abstract: Abstract Let n be a fixed positive integer, R be a prime ring, D and G two derivations of R and L a noncentral Lie ideal of R. Suppose that there exists 0 ≠ a ∈ R such that a(D(u)u n −u n G(u)) = 0 for all u ∈ L, where n ≥ 1 is a fixed integer. Then one of the following holds: 1. D = G = 0, unless R satisfies s 4; 2. char (R) ≠ 2, R satisfies s 4, n is even and D = G; 3. char (R) ≠ 2, R satisfies s 4, n is odd and D and G are two inner derivations induced by b, c respectively such that b + c ∈ C; 4. char (R) = 2 and R satisfies s 4. We also investigate the case when R is a semiprime ring.

Keywords: Prime ring; derivation; extended centroid; Martindale quotient ring (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s13226-015-0166-z

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