Fields on the Bottom

Moshe Jarden, Carlos Videla

Research output: Contribution to journalArticlepeer-review


We denote the field of totally real numbers by Qtr. For a set S of prime numbers we let Q(S) be the maximal Galois extension of Q whose degree is divisible only by prime numbers in S. We prove that the field Qtr,S = Qtr ∩ Q(S) has no proper subfield M with [Qtr,S : M] < ∞.

Original languageEnglish
Pages (from-to)213-219
Number of pages7
JournalJournal de Theorie des Nombres de Bordeaux
Issue number1
StatePublished - 2016


  • Bottom theorem
  • Pythagorean field
  • Totally real number


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