Editing Ordered ring (section)

[[Image:Real number line.svg|thumb|right|350px|The [[real number]]s are an ordered ring which is also an [[ordered field]]. The [[integers]], a subset of the real numbers, are an ordered ring that is not an ordered field.]]

In [[abstract algebra]], an '''ordered ring''' is a (usually [[Commutative ring|commutative]]) [[ring (mathematics)|ring]] ''R'' with a [[total order]] ≤ such that for all ''a'', ''b'', and ''c'' in ''R'':<ref>{{citation | last=Lam | first=T. Y. | authorlink=Tsit Yuen Lam | title=Orderings, valuations and quadratic forms | series=CBMS Regional Conference Series in Mathematics | volume=52 | publisher=[[American Mathematical Society]] | year=1983 | isbn=0-8218-0702-1 | zbl=0516.12001 | url-access=registration | url=https://archive.org/details/orderingsvaluati0000lamt }}</ref>

* if ''a'' ≤ ''b'' then ''a'' + ''c'' ≤ ''b'' + ''c''.
* if 0 ≤ ''a'' and 0 ≤ ''b'' then 0 ≤ ''ab''.