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• W2216341753 abstract "Let RL denote the ring of continuous real-valued functions on a completely regular frame L . The support of an α ∈ RL is the closed quotient ↑(coz α  ). We show that if supports are coz-quotients in L , then the set of functions with realcompact support is an ideal. If L satises the stronger condition that supports are C -quotients, then this ideal is the intersection of pure parts of the free maximal ideals of RL . The set of functions whose cozeroes are realcompact is always an ideal, which is free if and only if L is locally realcompact if and only if L is (isomorphic to) an open quotient of υ L . Further, this ideal is prime if and only if it is a free real maximal ideal if and only if υ L → L is a one-point extension of L . Keywords: Frame, ring of continuous real functions on a frame, support, realcompact support, locally realcompact frame,  Lindelof support" @default.
• W2216341753 created "2016-06-24" @default.
• W2216341753 creator A5016195169 @default.
• W2216341753 date "2015-12-04" @default.
• W2216341753 modified "2023-09-25" @default.
• W2216341753 title "Ideals associated with realcompactness in pointfree function rings" @default.
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• W2216341753 doi "https://doi.org/10.2989/16073606.2015.1015648" @default.
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