Hilbertianity of fields of power series

Elad Paran

doi:10.1017/S1474748011000144

Hilbertianity of fields of power series

Research output: Contribution to journal › Article › peer-review

Abstract

Let R be a domain contained in a rank-1 valuation ring of its quotient field. Let R[X] be the ring of formal power series over R, and let F be the quotient field of R[X]. We prove that F is Hilbertian. This resolves and generalizes an open problem of Jarden, and allows to generalize previous Galois-theoretic results over fields of power series.

Original language	English
Pages (from-to)	351-361
Number of pages	11
Journal	Journal of the Institute of Mathematics of Jussieu
Volume	11
Issue number	2
DOIs	https://doi.org/10.1017/S1474748011000144
State	Published - Apr 2012
Externally published	Yes

Keywords

AMS 2010 Mathematics subject classificationPrimary 12E30;

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1017/S1474748011000144

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title = "Hilbertianity of fields of power series",

abstract = "Let R be a domain contained in a rank-1 valuation ring of its quotient field. Let R[X] be the ring of formal power series over R, and let F be the quotient field of R[X]. We prove that F is Hilbertian. This resolves and generalizes an open problem of Jarden, and allows to generalize previous Galois-theoretic results over fields of power series.",

keywords = "AMS 2010 Mathematics subject classificationPrimary 12E30;",

author = "Elad Paran",

note = "Funding Information: Acknowledgements. The author was supported by an ERC grant while working on this research. The author thanks Arno Fehm, for many helpful suggestions and corrections, and the referee, for his/her comments.",

year = "2012",

month = apr,

doi = "10.1017/S1474748011000144",

language = "الإنجليزيّة",

volume = "11",

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PY - 2012/4

Y1 - 2012/4

N2 - Let R be a domain contained in a rank-1 valuation ring of its quotient field. Let R[X] be the ring of formal power series over R, and let F be the quotient field of R[X]. We prove that F is Hilbertian. This resolves and generalizes an open problem of Jarden, and allows to generalize previous Galois-theoretic results over fields of power series.

AB - Let R be a domain contained in a rank-1 valuation ring of its quotient field. Let R[X] be the ring of formal power series over R, and let F be the quotient field of R[X]. We prove that F is Hilbertian. This resolves and generalizes an open problem of Jarden, and allows to generalize previous Galois-theoretic results over fields of power series.

KW - AMS 2010 Mathematics subject classificationPrimary 12E30;

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DO - 10.1017/S1474748011000144

M3 - مقالة

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SP - 351

EP - 361

JO - Journal of the Institute of Mathematics of Jussieu

JF - Journal of the Institute of Mathematics of Jussieu

IS - 2

ER -

Hilbertianity of fields of power series

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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