# Bases of subalgebras of K[[x]] and K[x]

Abstract : Let $f_1,\ldots, f_s$ be formal power series (respectively polynomials) in the variable $x$. We study the semigroup of orders of the formal series in the algebra $K[[ f1,\ldots, f_s]] \subseteq K[[ x ]]$ (respectively the semigroup of degrees of polynomials in $K[f_1,\ldots,f_s]\subseteq K[x]$). We give procedures to compute these semigroups and several applications.
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Cited literature [19 references]

https://hal.archives-ouvertes.fr/hal-01094629
Contributor : Alain Monteil <>
Submitted on : Monday, August 29, 2016 - 11:02:23 AM
Last modification on : Monday, March 9, 2020 - 6:15:54 PM
Document(s) archivé(s) le : Wednesday, November 30, 2016 - 12:27:50 PM

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• HAL Id : hal-01094629, version 3
• ARXIV : 1412.4089

### Citation

Abdallah Assi, Pedro A. García-Sánchez, Vincenzo Micale. Bases of subalgebras of K[[x]] and K[x]. MEGA'2015 (Special Issue), Jun 2016, Trento, Italy. ⟨hal-01094629v3⟩

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