a little more on ideals associated with sublocales

As usual, let rl denote the ring of real-valued continuous functions on a completely regular frame l. let βl and λl denote the stone-čech compactification of l and the lindelöf coreflection of l, respectively. there is a natural way of associating with each sublocale of βl two ideals of rl, motivated by a similar situation in c(x). in [12], the authors go one step further and associate with each sublocale of λl an ideal of rl in a manner similar to one of the ways one does it for sublocales of βl. the intent in this paper is to augment [12] by considering two other coreflections; namely, the realcompact and the paracompact coreflections. we show that m-ideals of rl indexed by sublocales of βl are precisely the intersections of maximal ideals of rl. an m-ideal of rl is grounded in case it is of the form ms for some sublocale s of l. a similar definition is given for an o-ideal of rl. we characterise m-ideals of rl indexed by spatial sublocales of βl, and o-ideals of rl indexed by closed sublocales of βl in terms of grounded maximal ideals of rl.