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Gröbner bases in exterior algebra

✍ Scribed by Timothy Stokes

Publisher: Springer Netherlands
Year: 1990
Tongue: English
Weight: 784 KB
Volume: 6
Category: Article
ISSN: 0168-7433
DOI: 10.1007/bf00244487

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✦ Synopsis

We show that the Buchberger algorithm for commutative polynomials over a field may be generalised to an algebraic structure which embeds such polymomials, the exterior polynomial algebra, and which is a natural domain for linear geometry. In particular, those finite sets of exterior polynomials which induce confluent reduction relations are characterised, and a means of algorithmically constructing them from a given set presented. A distinguished subset of such bases consists of the exterior algebra version of Grrbner bases. We charaeterise such bases and demonstrate how to construct them algorithmically from a given finite set of exterior polynomials.

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