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Characterizing the multiplicative group of a real closed field in terms of its divisible maximal subgroup

Mahdavi Hezavehi, M ; Sharif University of Technology | 2009

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  1. Type of Document: Article
  2. Publisher: 2009
  3. Abstract:
  4. Let F be a field and M be a maximal subgroup of the multiplicative group F* = F {0} of index p. It is proved that if M is divisible, then Br(F)p ≠ 0 if and only if p = 2 and F is Euclidean. Furthermore, it is shown that in this case F* contains a divisible maximal subgroup if and only if F* is isomorphic to the multiplicative group of a real closed field. © 2009 Iranian Mathematical Society
  5. Keywords:
  6. Divisible subgroup ; Maximal
  7. Source: Bulletin of the Iranian Mathematical Society ; Volume 35, Issue 1 , 2009 , Pages 175-178 ; 10186301 (ISSN)
  8. URL: http://bims.iranjournals.ir/article_56.html