Abstract
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.
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