Journal of Formalized Mathematics
Volume 12, 2000
University of Bialystok
Copyright (c) 2000 Association of Mizar Users

Hilbert Basis Theorem


Jonathan Backer
University of Alberta, Edmonton
Piotr Rudnicki
University of Alberta, Edmonton

Summary.

We prove the Hilbert basis theorem following [7], page 145. First we prove the theorem for the univariate case and then for the multivariate case. Our proof for the latter is slightly different than in [7]. As a base case we take the ring of polynomilas with no variables. We also prove that a polynomial ring with infinite number of variables is not Noetherian.

This work has been partially supported by NSERC grant OGP9207.

MML Identifier: HILBASIS

The terminology and notation used in this paper have been introduced in the following articles [31] [11] [38] [18] [19] [33] [13] [39] [17] [9] [5] [20] [6] [27] [34] [3] [40] [35] [10] [15] [32] [12] [14] [37] [2] [28] [30] [22] [26] [36] [24] [25] [23] [1] [16] [8] [4] [21] [29]

Contents (PDF format)

  1. Preliminaries
  2. On Ring Isomorphism
  3. Hilbert Basis Theorem

Bibliography

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Received November 27, 2000

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