期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2013
卷号：2013
DOI：10.1155/2013/635361
出版社：Hindawi Publishing Corporation
摘要：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 .
