Prime Lie Rings of Derivations of Commutative Rings II

Lee, Pjek Hwee; Liu, Cheng-Kai

doi:10.1080/00927870601142108

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“…Any unexplained terminology is standard as in [1,4,9,13]. Many authors have investigated Lie rings of derivations Der R of differentially prime and differentially semiprime rings R. In this way, Jordan and Jordan [14,15], Nowicki [19], Chebotar and Lee [6], Lee and Liu [16]…”

Section: Introductionmentioning

confidence: 99%

Derivations of differentially semiprime rings

Khalaf

Taha

Artemovych

et al. 2019

Asian-European J. Math.

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Earlier D. A. Jordan, C. R. Jordan and D. S. Passman have investigated the properties of Lie rings Der [Formula: see text] of derivations in a commutative differentially prime rings [Formula: see text]. We study Lie rings Der [Formula: see text] in the non-commutative case and prove that if [Formula: see text] is a [Formula: see text]-torsion-free [Formula: see text]-semiprime ring, then [Formula: see text] is a semiprime Lie ring or [Formula: see text] is a commutative ring.

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