### Abstract

Let R be a 2-torsion free commutative ring with involution, and δ a nonzero derivation of R. Let S be the set of symmetric elements in R, and let K be the set of anti-symmetric elements in R. In this article, we investigate the semiprimeness of the Lie rings Sδ when δ is symmetric and Kδ when δ is anti-symmetric.

Original language | English |
---|---|

Pages (from-to) | 1747-1756 |

Number of pages | 10 |

Journal | Communications in Algebra |

Volume | 42 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2014 Jan 1 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Cite this

*Communications in Algebra*,

*42*(4), 1747-1756. https://doi.org/10.1080/00927872.2012.749261

}

*Communications in Algebra*, vol. 42, no. 4, pp. 1747-1756. https://doi.org/10.1080/00927872.2012.749261

**Semiprime Lie Rings of (Anti-)Symmetric Derivations of Commutative Rings.** / Liu, Cheng Kai; Liau, Pao Kuei.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Semiprime Lie Rings of (Anti-)Symmetric Derivations of Commutative Rings

AU - Liu, Cheng Kai

AU - Liau, Pao Kuei

PY - 2014/1/1

Y1 - 2014/1/1

N2 - Let R be a 2-torsion free commutative ring with involution, and δ a nonzero derivation of R. Let S be the set of symmetric elements in R, and let K be the set of anti-symmetric elements in R. In this article, we investigate the semiprimeness of the Lie rings Sδ when δ is symmetric and Kδ when δ is anti-symmetric.

AB - Let R be a 2-torsion free commutative ring with involution, and δ a nonzero derivation of R. Let S be the set of symmetric elements in R, and let K be the set of anti-symmetric elements in R. In this article, we investigate the semiprimeness of the Lie rings Sδ when δ is symmetric and Kδ when δ is anti-symmetric.

UR - http://www.scopus.com/inward/record.url?scp=84890540669&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84890540669&partnerID=8YFLogxK

U2 - 10.1080/00927872.2012.749261

DO - 10.1080/00927872.2012.749261

M3 - Article

AN - SCOPUS:84890540669

VL - 42

SP - 1747

EP - 1756

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 4

ER -