A Quadratic Differential Identity with Generalized Derivations on Multilinear Polynomials in Prime Rings

作者：Rania Francesco^*; Scudo Giovanni

来源：Mediterranean Journal of Mathematics, 2014, 11(2): 273-285.

DOI：10.1007/s00009-013-0331-8

• Prime rings
• differential identities
• generalized derivations

Let R be a prime ring of characteristic different from 2, with right Utumi quotient ring U and extended centroid C, and let f(x(1), ... , x(n)) be a multilinear polynomial over C, not central valued on R. Suppose that d is a derivation of R and G is a generalized derivation of R such that %26lt;br%26gt;C(r(1), ... , r(n)))d(f(r(1), ... ,r(n)) vertical bar d(f(r(1), ... , r(n)))C(f(r(1), ... , r(n))) = 0 %26lt;br%26gt;for all r(1), ... , r(n) epsilon R. Then either d = 0 or G = 0, unless when d is an inner derivation of R, there exists lambda epsilon C such that G(x) =lambda x, for all x epsilon R and f( x(1), ... , x(n))(2) is central valued on R.

• 出版日期2014-5