| Autor: |
Ighedo, O., Kivunga, G. W., Stephen, D. N. |
| Předmět: |
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| Zdroj: |
Categories & General Algebraic Structures with Applications; Jan2024, Vol. 20 Issue 1, p175-199, 26p |
| Abstrakt: |
As usual, let RL denote the ring of real-valued continuous functions on a completely regular frame L. Let ßL and λL denote the Stone-Cech compactification of L and the Lindel of coreflection of L, respectively. There is a natural way of associating with each sublocale of ßL 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 βL an ideal of RL in a manner similar to one of the ways one does it for sublocales of ßL. 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 ßL are precisely the intersections of maximal ideals of RL. AnM-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 ßL, and O-ideals of RL indexed by closed sublocales of ßL in terms of grounded maximal ideals of RL. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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