A classical result of Posner states that the existence of a nonzero centralizing derivation on a prime ring forces the ring to be commutative. In this paper we extend Posner's result to generalized derivations centralizing on Jordan ideals of rings with involution and discuss the related results. Moreover, we provide examples to show that the assumed restriction cannot be relaxed.
Rings with involution, generalized derivations, Jordan ideals
OUKHTITE, LAHCEN and MAMOUNI, ABDELLAH
"Generalized derivations centralizing on Jordan ideals of rings with involution,"
Turkish Journal of Mathematics: Vol. 38:
2, Article 4.
Available at: https://journals.tubitak.gov.tr/math/vol38/iss2/4