Powers of totally positive subgroups of fields

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For a formally real field F, a totally positive co-torsion subgroup S of F× and m ≥ 1, we prove that (∑ S)m ⊆ ∑ Sm. This extends a result of Becker. We prove several refinements of this fact related to higher Pythagoras numbers, real holomorphy rings, and sums with mixed powers.

Original languageEnglish
Pages (from-to)3104-3112
Number of pages9
JournalJournal of Algebra
Issue number8
StatePublished - 15 Oct 2008


  • Powers
  • Pythagoras numbers
  • Real holomorphy ring
  • Valuations
  • Waring problem

ASJC Scopus subject areas

  • Algebra and Number Theory


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