Abstract
In this article it is shown that the maximal quotient ringQA of a commutative semiprimef-ringA can be obtained by the formation of the orthocompletion ofA, followed by that of the classical quotient ring; for archimedeanf-rings the order of these can be inverted. It is shown that ifC=C(X, Z), whereX is a zero-dimensional Hausdorff space, then the integral closure is the Dedekind-McNeille completion ofC. The paper closes with a number of observations and examples.
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