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  "body": "\n## Summary\n\nA partially ordered ring is a [[ring|0B1261B5ED]] with a [[partial order|0QV2JS9RJ3]] that is preserved by addition and for which products of nonnegative elements are nonnegative.\nRings of real functions with the pointwise order and rings of real matrices with the entrywise order are typical examples.\n[[Ordered rings|H6WXC7Q71A]] are the case of a total order, and [[f-rings|VHHMZPNVEA]] are an important class of lattice-ordered rings.\n\n## Explanations\n\n### L1 human\n\nReal functions on a set can be added, multiplied and compared point by point.\nIf $f \\le g$, then $f + h \\le g + h$, and the product of two nonnegative functions is nonnegative.\nBut two functions need not be comparable: one may be larger at some points and smaller at others.\nA partially ordered ring is a ring with an order of this kind.\n",
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