A NOTE ON CERTAIN CENTRAL DIFFERENTIAL IDENTITIES WITH GENERALIZED DERIVATIONS

作者：Argac Nurcan^*; De Filippis Vincenzo

来源：Hacettepe Journal of Mathematics and Statistics, 2012, 41(6): 847-852.

• Prime rings
• Differential identities
• Generalized derivations

Let R be a noncommutatiye prime ring of characteristic different from 2 with right Utumi quotient ring U and extended centroid C, I a nonzero right ideal of R. Let f(x(1), . . ., x(n)) be a non-central multilinear polynomial over C, m %26gt;= 1 a fixed integer, a a fixed element of R, G a non-zero generalized derivation of R. If aG(f(r(1), . . ., r(n)))(m) is an element of Z(R) for all r(1), . . ., r(n) is an element of I, then one of the following holds: %26lt;br%26gt;(1) aI = aG(I) = (0); %26lt;br%26gt;(2) G(x) = qx, for some q is an element of U and aqI = 0; %26lt;br%26gt;(3) [f (x(1), . . ., x(n)), x(n+1)]x(n+2) is an identity for I; %26lt;br%26gt;(4) G(x) = cx + [q, x] for all x is an element of R, where c, q is an element of U such that cI = 0 and [q, I]I =

• 出版日期2012-12