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

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