×

Algebraic elements in formal power series rings. (English) Zbl 0675.13015

Let k be a perfect field of characteristic p. A set A of additive endomorphisms of k((x)) is defined such that an element f of k((x)) is algebraic over k(x) if and only if f is contained in an A-stable finite- dimensional k-vectorsubspace of k((x)). Other known characterizations of algebraicity are derived from this.
Reviewer: J.H.de Boer

MSC:

13F25 Formal power series rings
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] G. Christol, T. Kamae, M. Mendes-France et G. Rauzy,Suites algebraiques, automates et substitutions, Bull. Soc. Math. France108 (1980), 401–419. · Zbl 0472.10035
[2] P. Deligne,Integration sur un cycle evanescent, Invent. Math.76 (1983), 129–143. · Zbl 0538.13007
[3] M. Fliess,Sur divers products de series formelles, Bull. Soc. Math. France102 (1974), 181–191. · Zbl 0313.13021
[4] H. Furstenberg,Algebraic functions over finite fields, J. Algebra7 (1967), 271–277. · Zbl 0175.03903
[5] H. Kurke, G. Pfister und M. Roczen,Henselsche Ring und algebraische Geometrie, VEB Deutscher Verlag der Wissenschaften, Berlin, 1975.
[6] M. Mendes-France and A. J. Van der Poorten,Automata and the arithmetic of formal power series, Acta Arithmetica46 (1986), 211–214.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.