✦ LIBER ✦

Standard Bases in Power Series Rings: Uniqueness and Superfluous Critical Pairs

✍ Scribed by Thomas Becker

Publisher: Elsevier Science
Year: 1993
Tongue: English
Weight: 428 KB
Volume: 15
Category: Article
ISSN: 0747-7171
DOI: 10.1006/jsco.1993.1018

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✦ Synopsis

We show that w.r.t. fixed admissible term order, every ideal in a ring of power series over a field has a unique reduced standard basis. Furthermore, we show that a finite set of power series whose lowest terms are pairwise relatively prime is a standard basis. Finally, a second criterion for detecting superfluous critical pairs is discussed. As a spinoff, we obtain a Gröbner basis criterion that does not seem to have been stated before.