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ordered ring
In abstract algebra, an ordered ring is a (usually commutative) ring ''R'' with a total order ≤ such that for all ''a'', ''b'', and ''c'' in ''R'':〔 〕
* if ''a'' ≤ ''b'' then ''a'' + ''c'' ≤ ''b'' + ''c''.
* if 0 ≤ ''a'' and 0 ≤ ''b'' then 0 ≤ ''ab''.
==Examples==
Ordered rings are familiar from arithmetic. Examples include the integers, the rationals and the real numbers.〔
*
〕 (The rationals and reals in fact form ordered fields.) The complex numbers, in contrast, do not form an ordered ring or field, because there is no inherent order relationship between the elements 1 and ''i''.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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