Abstract
It is shown that certain partially ordered rings, defined by some of the properties of the totally ordered ring of integers, are exactly the bounded Z-rings, that is, the commutative f-rings with strong singular unit. The partially ordered rings in question amount to a discrete version of the rings introduced by M.H. Stone for his abstract characterization of the rings of real-valued continuous functions on compact Hausdorff spaces, and the function rings they correspond to are given by the integer-valued continuous functions on Boolean spaces.
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References
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Banaschewski, B. Integral Stone Rings. Order 22, 185–190 (2005). https://doi.org/10.1007/s11083-005-9016-7
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DOI: https://doi.org/10.1007/s11083-005-9016-7