This paper primarily provides a description of all compactifications of a completely regular frame L in terms of certain sub-l-rings of the l-ring RL of its real-valued continuous functions, and then obtains the corresponding result in the setting of zero-dimensional frames where the integer-valued continuous functions play the relevant role. Further, the related classical description of the compactification of a Tychonoff space is shown to be a straightforward consequence of the present pointfree result. The basic tool used here is the adjointness of the function ring functors involved - a feature not considered in the classical case.
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