### 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 |
---|---|

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 |

### Fingerprint

### Keywords

- Derivations
- Lie rings
- Prime Lie rings

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Journal of Algebra*,

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

**Prime Lie rings of derivations of commutative rings in characteristic 2.** / Liu, Chia-Hsin; Passman, Donald S.

Research output: Contribution to journal › Article

*Journal of Algebra*, vol. 311, no. 1, pp. 352-364. https://doi.org/10.1016/j.jalgebra.2006.08.035

}

TY - JOUR

T1 - Prime Lie rings of derivations of commutative rings in characteristic 2

AU - Liu, Chia-Hsin

AU - Passman, Donald S.

PY - 2007/5/1

Y1 - 2007/5/1

N2 - 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.

AB - 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.

KW - Derivations

KW - Lie rings

KW - Prime Lie rings

UR - http://www.scopus.com/inward/record.url?scp=33947315952&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33947315952&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2006.08.035

DO - 10.1016/j.jalgebra.2006.08.035

M3 - Article

AN - SCOPUS:33947315952

VL - 311

SP - 352

EP - 364

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

IS - 1

ER -