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  "body": "\n## Summary\n\nAn f-ring is a lattice-ordered ring in which multiplying by a nonnegative element keeps disjoint elements disjoint.\nThe notion was introduced by Birkhoff and Pierce.\nRings of continuous real functions with the pointwise order, and products of totally ordered rings, are f-rings.\nEvery f-ring is a subdirect product of totally ordered rings, so f-rings behave in many ways like rings of real functions.\n\n## Explanations\n\n### L1 human\n\nTwo nonnegative functions are disjoint when at each point at least one of them is zero.\nIf you multiply one of them by any nonnegative function, it stays zero where it was zero, so the two stay disjoint.\nAn f-ring is a ring with a lattice order in which this property holds.\nThe letter f stands for function, since these rings behave like rings of functions.\n",
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