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Zbl 0705.16021
Bell, H.E.; Kappe, L.C.
Rings in which derivations satisfy certain algebraic conditions. (English)
[J] Acta Math. Hung. 53, No.3-4, 339-346 (1989). ISSN 0236-5294; ISSN 1588-2632/e

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.
[S.K.Jain]

MSC 2000:: *16U70 Commutativity theorems for assoc. rings
16N60 Prime and semiprime assoc. rings
16W25 Derivations, actions of Lie algebras (assoc. rings and algebras)

Keywords: commutator conditions; inner derivations; PD-rings; semiprime ring

Cited in: Zbl 1072.16039 Zbl 1053.16025 Zbl 1048.06012 Zbl 1030.16020 Zbl 0963.16031 Zbl 0898.16030

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