## A constructive version of Hilbert's basis theorem |

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### Contents

A Constructive Basis Theorem for Discrete | 13 |

2 The Noetherian Condition | 19 |

4 The Direct Sum Theorem | 28 |

3 other sections not shown

### Common terms and phrases

a. e. c. sequence a. e. c. test sequence Algebra allowable basis operation allowable operation Chapter classical coef coef(d coefficients column sequence constructively Corollary deg f denote Direct Sum Theorem dN+1 equations equivalent Errett Bishop eventually constant exceptional index exists a basis exists an a. e. c. finite number following property free abelian group given sequence gN+l Goldbach's conjecture Hence Hilbert's Basis Theorem hypothesis ideal induction infinite matrix infinite sequence Lemma 18 Lemma 20 Lemma 9 linear combination max deg(m n-tuple n+1 n+1 Noetherian basis operation Noetherian condition Noetherian module Noetherian property Noetherian ring nonnegative integers operation cp operation for M[x operation Rd paragraph Proposition prove real numbers Reduction Theorem satisfy saturated set sensible module sensible set sequence f sequence of integers statement Suppose true degree weakly bounded zero