Centralizing and commuting generalized derivations on prime rings. (English) Zbl 1187.16036

Ali, Asif; Shah, Tariq

Mat. Vesn. 60, No. 1, 1-2 (2008).

Summary: Let \(R\) be a prime ring and \(d\) a derivation on \(R\). If \(f\) is a generalized derivation on \(R\) such that \(f\) is centralizing on a left ideal \(U\) of \(R\), then \(R\) is commutative.

MSC:

16W25	Derivations, actions of Lie algebras
16N60	Prime and semiprime associative rings
16U70	Center, normalizer (invariant elements) (associative rings and algebras)
16U80	Generalizations of commutativity (associative rings and algebras)

Keywords:

prime rings; generalized derivations; centralizing maps; commutativity theorems; commuting maps