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Journal de Théorie des Nombres de Bordeaux
Article . 2008 . Peer-reviewed
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Journal de Théorie des Nombres de Bordeaux
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https://dx.doi.org/10.5802/jtn...
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PAC fields over number fields

descriptionPublicationkeyboard_double_arrow_right Article 02 Dec 2008 English Publisher:MathDoc/Centre MersenneJournal:Journal de théorie des nombres de Bordeaux, volume 18, pages 371-377 (eissn: 2118-8572, Copyright policy )
Authors: Jarden, Moshe;

doi: 10.5802/jtnb.550

PAC fields over number fields

Abstract

We prove that if K is a number field and N is a Galois extension of ℚ which is not algebraically closed, then N is not PAC over K .

Keywords

field arithmetic, Field arithmetic, PAC fields

  • BIP!
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    selected citations
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    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 3
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    		 Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 Average
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    		 Average
Powered by OpenAIRE graph
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
3
Average
Average
Average
gold