Abstract
In this paper we extend the techniques and the basic results of the classical Galois theory of the fields extension 
is an algebraic closure of Q, to the algebras extension ℝ ⊂ ℂsym(G), where this last is the ℝ— algebra of all the continuous symmetric functions ƒ defined on the absolute Galois group 
with values in ℂ.
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Popescu, A., Popescu, N. & Zaharescu, A. A galois theory for the banach algebra of continuous symmetric functions on absolute galois groups. Results. Math. 45, 349–358 (2004). https://doi.org/10.1007/BF03323388
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DOI: https://doi.org/10.1007/BF03323388