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Ordered Rings and Fields

100%

Schwarzweller C.

Formalized Mathematics

2017

tom 25

nr 1

63-72

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].

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O ciałach uporządkowanych

88%

Błaszczyk P.

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

2012

tom 4

15-30

In this paper, we present some basic facts concerning ordered fields. We review definitions of an ordered field, give an example of a field that admits many orderings, and present equivalent definitions of the axiom of Archimedes and the continuity axiom. We show how to extend an ordered field by means of an ultrapower construction and formal power series.

Ograniczanie wyników

1 Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

1 Formalized Mathematics

1 Błaszczyk P.

1 Schwarzweller C.

1 2017

1 2012

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Ordered Rings and Fields

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