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Title

ON MAXIMAL IDEALS OF R∞ L

Pages

 Start Page 43 | End Page 57

Abstract

 Let L be a completely regular Frame and RL be the ring of real-valued continuous functions on L. We consider the set R1L = {φ ∈ RL: ↑ φ ( − 1 n, 1 n ) is a Compact Frame for any n ∈ N}. Suppose that C1(X) is the family of all functions f ∈ C(X) for which the set {x ∈ X: |f(x)| ≥ 1 n } is Compact, for every n ∈ N. Kohls has shown that C1(X) is precisely the intersection of all the free Maximal ideals of C (X). The aim of this paper is to extend this result to the real continuous functions on a Frame and hence we show that R1L is precisely the intersection of all the free Maximal ideals of R L. This result is used to characterize the Maximal ideals in R1L.

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