## Abstract

In this paper we generalize some basic applications of Gröbner bases

in commutative polynomial rings to the non-commutative case. We define

a non-commutative elimination order. Methods

of finding the intersection of two ideals are given. If both the

ideals are monomial we deduce a finitely written basis for their intersection. We find the kernel of a

homomorphism, and decide membership of the image. Finally we show how to obtain a Gröbner basis for an

ideal by considering a related homogeneous ideal.

in commutative polynomial rings to the non-commutative case. We define

a non-commutative elimination order. Methods

of finding the intersection of two ideals are given. If both the

ideals are monomial we deduce a finitely written basis for their intersection. We find the kernel of a

homomorphism, and decide membership of the image. Finally we show how to obtain a Gröbner basis for an

ideal by considering a related homogeneous ideal.

Original language | English |
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Title of host publication | London Math. Soc. Lecture Note Ser. |

Editors | Bruno Buchberger, Franz Winkler |

Publisher | Cambridge University Press |

Pages | 463-472 |

Volume | 251 |

ISBN (Print) | 0-521-63298-6 |

Publication status | Published - 1998 |

Event | 33 Years of Gröbner Bases - Linz Duration: 1998 Feb 2 → … |

### Publication series

Name | |
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Volume | 251 |

### Conference

Conference | 33 Years of Gröbner Bases |
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Period | 1998/02/02 → … |

## Subject classification (UKÄ)

- Mathematics