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  "body": "\n## Summary\n\nAn ordered ring is a commutative [[ring|0B1261B5ED]] with a [[total order|0FRXBVVR03]] that is preserved by addition and for which products of nonnegative elements are nonnegative.\nThe integers are the basic example, and every [[ordered field|0P3VCBDEE2]] is an ordered ring.\nIn an ordered ring every square is nonnegative, and the usual rules for inequalities hold.\n\n## Explanations\n\n### L1 human\n\nThe integers can be added, multiplied and compared, and the familiar rules link these operations.\nAdding the same number to both sides of an inequality keeps it true.\nThe product of two nonnegative numbers is nonnegative.\nAn ordered ring is any ring with an order that obeys these rules, such as the integers, the rationals or the polynomials with the right order.\n",
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