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. 
@article{AL_2009_48_6_a2,
     author = {Yu. L. Ershov},
     title = {Subfields of the adele ring},
     journal = {Algebra i logika},
     pages = {741--753},
     publisher = {mathdoc},
     volume = {48},
     number = {6},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2009_48_6_a2/}
}
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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/