### Abstract

Let R be a commutative associative ring with 1 and let Der (R) be the Lie ring of all derivations of R. Suppose that D is a Lie subring and an R-submodule of Der (R). When R is D-prime, we give necessary and sufficient conditions for D to be Lie prime. Since results of this nature are already known for rings R of characteristic different from 2, what is really new here is the characteristic 2 case.

Original language | English |
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Pages (from-to) | 352-364 |

Number of pages | 13 |

Journal | Journal of Algebra |

Volume | 311 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2007 May 1 |

### Keywords

- Derivations
- Lie rings
- Prime Lie rings

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Liu, C-H., & Passman, D. S. (2007). Prime Lie rings of derivations of commutative rings in characteristic 2.

*Journal of Algebra*,*311*(1), 352-364. https://doi.org/10.1016/j.jalgebra.2006.08.035