Demir, C.Argac, N.2019-10-272019-10-2720111005-38671005-3867https://doi.org/10.1142/S1005386711000861https://hdl.handle.net/11454/45833Let K be a commutative ring with unit, R be a prime K-algebra with center Z(R), right Utumi quotient ring U and extended centroid C, and I a nonzero right ideal of R. Let g be a nonzero generalized derivation of R and f(X(1), ... , X(n)) a multilinear polynomial over K. If g(f(x(1,) ... , x(n) ))f(x(1), ... , x(n)) is an element of C for all x(1), ... , x(n) is an element of I, then either f(x1, ... , ) x(n) (+ 1) is an identity for I, or char(R) = 2 and R satisfies the standard identity s(4)(x(1), ... , x(4)), unless when g(x) = ax [x, b] for suitable a, b is an element of U and one of the following holds: (i) a, b is an element of C and f, x)2 is central valued on R; (ii) a is an element of C and f(x(1), ... , x(n)) is central valued on R; (iii) aI = 0 and [f(x(1) , ... , x(n)), x(n + 1)]x(n +) (2) is an identity for I; (iv) aI = 0 and (b - beta)I = 0 for some beta is an element of C.en10.1142/S1005386711000861info:eu-repo/semantics/closedAccessprime ring(generalized) derivationright Utumi quotient ringdifferential identitygeneralized polynomial identityArticle18987998WOS:000297061400028Q4