Title | **Grobner-Shirshov Bases for Dialgebras** |

Author(s) | Leonid A. Bokut, yugon Chen, Cihua Liu |

Type | Article in Journal |

Abstract | In this paper, we define the Gröbner–Shirshov basis for a dialgebra. The Composition–Diamond lemma for dialgebras is given then. As a result, we give Gröbner–Shirshov bases for the universal enveloping algebra of a Leibniz algebra, the bar extension of a dialgebra, the free product of two dialgebras, and Clifford dialgebra. We obtain some normal forms for algebras mentioned the above. |

Keywords | Dialgebra; Gröbner–Shirshov basis; Leibniz algebra; Clifford dialgebra |

URL |
DOI: 10.1142/S0218196710005753 |

Language | English |

Journal | International Journal of Algebra and Computation (IJAC) |

Volume | 20 |

Number | 3 |

Pages | 391-415 |

Year | 2010 |

Translation |
No |

Refereed |
Yes |

Sponsors | Supported by the NNSF of China (Nos. 10771077, 10911120389) and the NSF of Guangdong Province (No. 06025062) |