Title | **The Membership Problem for finitely generated quadratic modules in the univariate case** |

Author(s) | Doris Augustin |

Type | Article in Journal |

Abstract | We prove that the Membership Problem is solvable affirmatively for every finitely generated quadratic module Q of R [ X 1 ] . For the case that the associated semialgebraic set S is bounded we show that a polynomial f is an element of Q if and only if f is nonnegative on S and fulfills certain order conditions in the boundary points of S . This leads us to the definition of generalized natural generators of the quadratic module Q . |

ISSN | 0022-4049 |

URL |
http://www.sciencedirect.com/science/article/pii/S0022404912000436 |

Language | English |

Journal | Journal of Pure and Applied Algebra |

Volume | 216 |

Number | 10 |

Pages | 2204 - 2212 |

Year | 2012 |

Edition | 0 |

Translation |
No |

Refereed |
No |