Bi-Condition of Existence for a Compatible Directed Order on an Arbitrary Field †

Niels Schwartz; Yi Chuan Yang

doi:10.3390/sym15010215

Bi-Condition of Existence for a Compatible Directed Order on an Arbitrary Field †

Niels Schwartz
, Yi Chuan Yang^*

^*Corresponding author for this work

School of Mathematical Sciences

University of Passau

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

Abstract

One proves that a field carries a compatible directed order if and only if it has characteristic 0 and is real or has a transcendence degree of at least 1 over the field of rational numbers.

Original language	English
Article number	215
Journal	Symmetry
Volume	15
Issue number	1
DOIs	https://doi.org/10.3390/sym15010215
State	Published - Jan 2023

Keywords

Archimedean partial order
Dedekind cut
algebraic extension
partially ordered field
real field
strong unit
strongly Archimedean partial order
totally ordered field
totally ordered ring

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title = "Bi-Condition of Existence for a Compatible Directed Order on an Arbitrary Field †",

abstract = "One proves that a field carries a compatible directed order if and only if it has characteristic 0 and is real or has a transcendence degree of at least 1 over the field of rational numbers.",

keywords = "Archimedean partial order, Dedekind cut, algebraic extension, partially ordered field, real field, strong unit, strongly Archimedean partial order, totally ordered field, totally ordered ring",

author = "Niels Schwartz and Yang, \{Yi Chuan\}",

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doi = "10.3390/sym15010215",

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AB - One proves that a field carries a compatible directed order if and only if it has characteristic 0 and is real or has a transcendence degree of at least 1 over the field of rational numbers.

KW - Archimedean partial order

KW - Dedekind cut

KW - algebraic extension

KW - partially ordered field

KW - real field

KW - strong unit

KW - strongly Archimedean partial order

KW - totally ordered field

KW - totally ordered ring

UR - https://www.scopus.com/pages/publications/85146762939

U2 - 10.3390/sym15010215

DO - 10.3390/sym15010215

M3 - 文章

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SN - 2073-8994

VL - 15

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ER -

Bi-Condition of Existence for a Compatible Directed Order on an Arbitrary Field †

Abstract

Keywords

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