Powers of totally positive subgroups of fields

Ido Efrat

doi:10.1016/j.jalgebra.2008.06.037

Powers of totally positive subgroups of fields

Ido Efrat

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

For a formally real field F, a totally positive co-torsion subgroup S of F^× and m ≥ 1, we prove that (∑ S)^m ⊆ ∑ S^m. 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
Pages (from-to)	3104-3112
Number of pages	9
Journal	Journal of Algebra
Volume	320
Issue number	8
DOIs	https://doi.org/10.1016/j.jalgebra.2008.06.037
State	Published - 15 Oct 2008

Keywords

Powers
Pythagoras numbers
Real holomorphy ring
Valuations
Waring problem

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2008.06.037

Cite this

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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.",

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N2 - 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.

AB - 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.

KW - Powers

KW - Pythagoras numbers

KW - Real holomorphy ring

KW - Valuations

KW - Waring problem

UR - https://www.scopus.com/pages/publications/51249101076

U2 - 10.1016/j.jalgebra.2008.06.037

DO - 10.1016/j.jalgebra.2008.06.037

M3 - Article

AN - SCOPUS:51249101076

SN - 0021-8693

VL - 320

SP - 3104

EP - 3112

JO - Journal of Algebra

JF - Journal of Algebra

IS - 8

ER -

Powers of totally positive subgroups of fields

Abstract

Keywords

ASJC Scopus subject areas

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