Numerical Semigroups and Applications by Abdallah Assi & Pedro A. García-Sánchez

Author:Abdallah Assi & Pedro A. García-Sánchez
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Thus we have an algorithmic method to calculate approximate roots of f. As a consequence we will be able to compute for , and thus the semigroup associated to f.

Proposition 30

Let the notations be as above. For all ,

Proof

Let and let be a pseudo-approximate root of f. Uniqueness in Lemma 19 allows us to repeat the first part of the proof starting with instead of . By Proposition 28, . But can be obtained by applying the operation finitely many times to . Hence the result is a consequence of Proposition 29 and Corollary 13.

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