Rings in which derivations satisfy certain algebraic conditions. (English) Zbl 0705.16021

The purpose of this paper is to investigate some commutator conditions for rings. Rings in which all inner derivations are potent are called PD- rings. Following are some of the results proved: (1) Let R be a semiprime ring. If d is a derivation of R which is either an endomorphism or an anti-endomorphism, then \(d=0\). (2) Let R be a prime ring and U a nonzero right ideal of R. If d is a derivation of R which acts as a homomorphism or an anti-homomorphism on U, then \(d=0\) on R. (3) Every PD-ring is commutative.
Reviewer: S.K.Jain


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