Abstract
This paper shows that the compact completely regular coreflection in the category of frames is given by the frame of Jacobson radical ideals of the ring R L of real-valued continuous functions on L , as an alternative to its familiar representations in terms of (i) the l -ideals of R L as lattice-ordered ring or (ii) the ideals of the bounded part of R L which are closed in the usual uniform topology. Further, in analogy with this, the compact zero-dimensional coreflection will also be described in terms of ring ideals, this time of the ring Z L of integer-valued continuous functions on L .
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