ordered ring

An ordered ring is a commutative ring R with a total ordering such that, for every a,b,cR:

  1. 1.

    If ab, then a+cb+c

  2. 2.

    If ab and 0c, then cacb

An ordered field is an ordered ring (R,) where R is also a field.

Examples of ordered rings include:

Examples of rings which do not admit any ordering relation making them into an ordered ring include:

Title ordered ring
Canonical name OrderedRing
Date of creation 2013-03-22 11:52:06
Last modified on 2013-03-22 11:52:06
Owner djao (24)
Last modified by djao (24)
Numerical id 13
Author djao (24)
Entry type Definition
Classification msc 06F25
Classification msc 12J15
Classification msc 13J25
Classification msc 11D41
Related topic TotalOrder
Related topic OrderingRelation
Defines ordered field