A result on generalized derivations on right ideals of prime rings
Articles > Article · 2012
Authors: Çağrı DEMİR, Nurcan ARGAÇ
UKRAINIAN MATHEMATICAL JOURNAL, Journal Indexed in SCI Expanded, International, 2012, vol 64, pp 186-197
DOI: 10.1007/s11253-012-0637-x
Summary
Let R be a prime ring of characteristic other than 2 and let I be a nonzero right ideal of R. Also let U be the right Utumi quotient ring of R and let C be the center of U. If G is a generalized derivation of R such that [[G(x), x], G(x)] = 0 for all x a I, then R is commutative or there exist a, b a U such that G(x) = ax + xb for all x a R and one of the following assertions is true: (1) (a - lambda)I = (0) = (b + lambda)I for some lambda epsilon C,