La clôture algébrique du corps des séries formelles

Benhissi, Ali

doi:10.5802/ambp.42

Cited by 3 publications

(3 citation statements)

References 4 publications

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“…Our results imply Theorem 2 as well as other results of Benhissi [2], Huang, and Vaidya [13]. (They do not directly imply Theorem 1, but our approach can be easily adapted to give a short proof of that theorem.…”

Section: Introductionsupporting

confidence: 72%

“…A prototype of the latter condition is the following result, also due independently to Huang and to Stefȃnescu [12]. Our main result (Theorem 8) implies Theorem 2 as well as other results of Benhissi [2], Huang, and Vaidya [13]. (It does not directly imply Theorem 1, but our approach can be easily adapted to give a short proof of that theorem.)…”

Section: There Exists a Natural Number M Such That Every Element Of Msupporting

confidence: 47%

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The algebraic closure of the power series field in positive characteristic

Kedlaya

2001

Proc. Amer. Math. Soc.

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Abstract. For K an algebraically closed field, let K((t)) denote the quotient field of the power series ring over K. The "Newton-Puiseux theorem" states that if K has characteristic 0, the algebraic closure of K((t)) is the union of the fields K((t 1/n )) over n ∈ N. We answer a question of Abhyankar by constructing an algebraic closure of K((t)) for any field K of positive characteristic explicitly in terms of certain generalized power series.

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Section: Introductionsupporting

confidence: 72%

Section: There Exists a Natural Number M Such That Every Element Of Msupporting

confidence: 47%

The algebraic closure of the power series field in positive characteristic

Kedlaya

2001

Proc. Amer. Math. Soc.

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“…The approach of studying the algebraic closure of k((x)) through generalized power series is developed by Benhessi [5], Hahn [12], Huang, [15], Poonen [21], Rayner [22], Stefanescu [26] and Vaidya [28]. A complete solution when k is a perfect field is given by Kedlaya in [16].…”

Section: Introductionmentioning

confidence: 99%

Algebraic series and valuation rings over nonclosed fields

Cutkosky

Kashcheyeva

2008

Journal of Pure and Applied Algebra

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Suppose that k is an arbitrary field. Let k[[x 1 , . . . , x n ]] be the ring of formal power series in n variables with coefficients in k. Let k be the algebraic closure of k and σ ∈ k[[x 1 , . . . , x n ]]. We give a simple necessary and sufficient condition for σ to be algebraic over the quotient field of k[[x 1 , . . . , x n ]]. We also characterize valuation rings V dominating an excellent Noetherian local domain R of dimension 2, and such that the rank increases after passing to the completion of a birational extension of R. This is a generalization of the characterization given by M. Spivakovsky [Valuations in function fields of surfaces, Amer. J. Math. 112 (1990) 107-156] in the case when the residue field of R is algebraically closed.

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The McDonald theorem in positive characteristic

Saavedra

2017

Journal of Algebra

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La clôture algébrique du corps des séries formelles

Cited by 3 publications

References 4 publications

The algebraic closure of the power series field in positive characteristic

The algebraic closure of the power series field in positive characteristic

Algebraic series and valuation rings over nonclosed fields

The McDonald theorem in positive characteristic

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