# Ordered Rings and Fields

Formalized Mathematics (2017)

- Volume: 25, Issue: 1, page 63-72
- ISSN: 1426-2630

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topChristoph Schwarzweller. "Ordered Rings and Fields." Formalized Mathematics 25.1 (2017): 63-72. <http://eudml.org/doc/288151>.

@article{ChristophSchwarzweller2017,

abstract = {We introduce ordered rings and fields following Artin-Schreier’s approach using positive cones. We show that such orderings coincide with total order relations and give examples of ordered (and non ordered) rings and fields. In particular we show that polynomial rings can be ordered in (at least) two different ways [8, 5, 4, 9]. This is the continuation of the development of algebraic hierarchy in Mizar [2, 3].},

author = {Christoph Schwarzweller},

journal = {Formalized Mathematics},

keywords = {commutative algebra; ordered fields; positive cones},

language = {eng},

number = {1},

pages = {63-72},

title = {Ordered Rings and Fields},

url = {http://eudml.org/doc/288151},

volume = {25},

year = {2017},

}

TY - JOUR

AU - Christoph Schwarzweller

TI - Ordered Rings and Fields

JO - Formalized Mathematics

PY - 2017

VL - 25

IS - 1

SP - 63

EP - 72

AB - We introduce ordered rings and fields following Artin-Schreier’s approach using positive cones. We show that such orderings coincide with total order relations and give examples of ordered (and non ordered) rings and fields. In particular we show that polynomial rings can be ordered in (at least) two different ways [8, 5, 4, 9]. This is the continuation of the development of algebraic hierarchy in Mizar [2, 3].

LA - eng

KW - commutative algebra; ordered fields; positive cones

UR - http://eudml.org/doc/288151

ER -

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