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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

MSC:
16U70Center, normalizer (invariant elements) for associative rings
16N60Prime and semiprime associative rings
16W25Derivations, actions of Lie algebras (associative rings and algebras)
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