## Abstract

Canonical bases, also called SAGBI bases, for subalgebras of

the non-commutative polynomial ring are investigated. The process of

subalgebra reduction is defined. Methods, including generalizations of

the standard Gröbner bases techniques, are developed for the test whether

bases are canonical, and for the completion procedure of constructing canonical

bases. The special case of homogeneous subalgebras is discussed.

the non-commutative polynomial ring are investigated. The process of

subalgebra reduction is defined. Methods, including generalizations of

the standard Gröbner bases techniques, are developed for the test whether

bases are canonical, and for the completion procedure of constructing canonical

bases. The special case of homogeneous subalgebras is discussed.

Original language | English |
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Title of host publication | Proceedings of the 1998 International Symposium on Symbolic and Algebraic Computation |

Editors | Oliver Gloor |

Publisher | Association for Computing Machinery (ACM) |

Pages | 140-146 |

ISBN (Print) | 1-58113-002-3 |

DOIs | |

Publication status | Published - 1998 |

Event | Proceedings of ISSAC '98. International Symposium on Symbolic and Algebraic Computation - Rostock Duration: 1998 Aug 13 → 1998 Aug 15 |

### Conference

Conference | Proceedings of ISSAC '98. International Symposium on Symbolic and Algebraic Computation |
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Period | 1998/08/13 → 1998/08/15 |

## Subject classification (UKÄ)

- Mathematics

## Free keywords

- polynomials
- non-commutative polynomial rings
- canonical bases
- SAGBI bases
- subalgebra reduction
- Grobner bases
- homogeneous subalgebras