Characterization and Existence of Gr\"obner Bases

Journal of Formalized Mathematics
Volume 15, 2003
University of Bialystok
Copyright (c) 2003 Association of Mizar Users

Characterization and Existence of Gr\"obner Bases

Christoph Schwarzweller: University of T\"ubingen

Summary.

We continue the Mizar formalization of Gr\"{o}bner bases following [8]. In this article we prove a number of characterizations of Gr\"{o}bner bases among them that Gr\"{o}bner bases are convergent rewriting systems. We also show the existence and uniqueness of reduced Gr\"{o}bner bases.

MML Identifier: GROEB_1

The terminology and notation used in this paper have been introduced in the following articles [24] [32] [34] [33] [10] [4] [18] [28] [11] [30] [12] [14] [5] [2] [31] [9] [7] [16] [17] [13] [21] [20] [25] [27] [19] [1] [6] [15] [23] [29] [26] [3] [22]

Contents (PDF format)

Preliminaries
Characterization of Gr\"{o}bner Bases
Existence of Gr\"{o}bner Bases

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Received June 11, 2003

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