Geodesic
Subfields of the adele ring
Algebra i logika, Tome 48 (2009) no. 6, pp. 741-753.

Voir la notice de l'article provenant de la source Math-Net.Ru

We establish a natural one-to-one correspondence between immediate extensions of a Dedekind ring and subfields of its ring of adeles containing its ring of fractions. As a consequence of the existence theorems for immediate extensions proved previously, we state that $e$-closed fields within the class of countable subfields of the classical adele ring are surprising extensions of the field of rationals.
Keywords: adele ring, Dedekind ring, immediate extension, surprising extension of field of rationals. 
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Yu. L. Ershov. Subfields of the adele ring. Algebra i logika, Tome 48 (2009) no. 6, pp. 741-753. http://geodesic.mathdoc.fr/item/AL_2009_48_6_a2/

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