GENERALIZED DERIVATIONS WITH LEFT ANNIHILATOR CONDITIONS IN PRIME AND SEMIPRIME RINGS
Journal Title: Discussiones Mathematicae - General Algebra and Applications - Year 2017, Vol 37, Issue 2
Abstract
Let R be a prime ring with its Utumi ring of quotients U, C = Z(U) be the extended centroid of R, H and G two generalized derivations of R, L a noncentral Lie ideal of R, I a nonzero ideal of R. The left annihilator of S ⊆ R is denoted by lR(S) and defined by lR(S) = {x ∈ R | xS = 0}. Suppose that S = {H(un)un + unG(un)| u ∈ L} and T = {H(xn)xn + xnG(xn)| x ∈I}, where n ≥ 1 is a fixed integer. In the paper, we investigate the cases when the sets lR(S) and lR(T ) are nonzero. Keywords: prime ring, derivation, Lie ideal, generalized derivation, extended centroid, Utumi quotient ring. 2010 Mathematics Subject Classification: 16W25, 16W80, 16N60.
Authors and Affiliations
Basudeb Dhara
Keywords
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