A Galois theory for the Banach algebra of continuous symmetric functions on absolute Galois groups

Angel Popescu; Nicolae Popescu; Alexandru Zaharescu

doi:10.1007/BF03323388

A Galois theory for the Banach algebra of continuous symmetric functions on absolute Galois groups

Angel Popescu, Nicolae Popescu, Alexandru Zaharescu

Mathematics

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

Abstract

In this paper we extend the techniques and the basic results of the classical Galois theory of the fields extension [InlineMediaObject not available: see fulltext.] is an algebraic closure of Q, to the algebras extension ℝ ⊂ ℂ _sym(G), where this last is the ℝ— algebra of all the continuous symmetric functions ƒ defined on the absolute Galois group [InlineMediaObject not available: see fulltext.] with values in ℂ.

Original language	English (US)
Pages (from-to)	349-358
Number of pages	10
Journal	Results in Mathematics
Volume	45
Issue number	3-4
DOIs	https://doi.org/10.1007/BF03323388
State	Published - May 1 2004

Keywords

Banach algebras
Galois groups
continuous functions
number fields

ASJC Scopus subject areas

Applied Mathematics
Mathematics (miscellaneous)

Online availability

10.1007/BF03323388

http://dx.doi.org/10.1007/BF03323388

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AB - In this paper we extend the techniques and the basic results of the classical Galois theory of the fields extension [InlineMediaObject not available: see fulltext.] is an algebraic closure of Q, to the algebras extension ℝ ⊂ ℂ sym(G), where this last is the ℝ— algebra of all the continuous symmetric functions ƒ defined on the absolute Galois group [InlineMediaObject not available: see fulltext.] with values in ℂ.

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KW - number fields

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A Galois theory for the Banach algebra of continuous symmetric functions on absolute Galois groups

Abstract

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