Abstract
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 language | English |
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Pages (from-to) | 3104-3112 |
Number of pages | 9 |
Journal | Journal of Algebra |
Volume | 320 |
Issue number | 8 |
DOIs | |
State | Published - 15 Oct 2008 |
Keywords
- Powers
- Pythagoras numbers
- Real holomorphy ring
- Valuations
- Waring problem
ASJC Scopus subject areas
- Algebra and Number Theory