Characterizations of Ideals in Intermediate -Rings via the -Compactifications of

Joshua Sack and Saleem Watson

International Journal of Mathematics and Mathematical Sciences, 2013, vol. 2013, 1-6

Abstract:

Let be a completely regular topological space. An intermediate ring is a ring of continuous functions satisfying . In Redlin and Watson (1987) and in Panman et al. (2012), correspondences and are defined between ideals in and -filters on , and it is shown that these extend the well-known correspondences studied separately for and , respectively, to any intermediate ring. Moreover, the inverse map sets up a one-one correspondence between the maximal ideals of and the -ultrafilters on . In this paper, we define a function that, in the case that is a -ring, describes in terms of extensions of functions to realcompactifications of . For such rings, we show that maps -filters to ideals. We also give a characterization of the maximal ideals in that generalize the Gelfand-Kolmogorov theorem from to .

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:635361

DOI: 10.1155/2013/635361

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