Characterizations of Ideals in Intermediate C-Rings A(X) via the A-Compactifications of X
Joint Authors
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-6, 6 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-07-17
Country of Publication
Egypt
No. of Pages
6
Main Subjects
Abstract EN
Let X be a completely regular topological space.
An intermediate ring is a ring A(X) of continuous functions satisfying C*(X)⊆A(X)⊆C(X).
In Redlin and Watson (1987) and in Panman et al.
(2012), correspondences ?A and ℨA are defined between ideals in A(X) and z-filters on X, and it is shown that these extend the well-known correspondences studied separately for C∗(X) and C(X), respectively, to any intermediate ring.
Moreover, the inverse map ?A← sets up a one-one correspondence between the maximal ideals of A(X) and the z-ultrafilters on X.
In this paper, we define a function ?A that, in the case that A(X) is a C-ring, describes ℨA in terms of extensions of functions to realcompactifications of X.
For such rings, we show that ℨA← maps z-filters to ideals.
We also give a characterization of the maximal ideals in A(X) that generalize the Gelfand-Kolmogorov theorem from C(X) to A(X).
American Psychological Association (APA)
Sack, Joshua& Watson, Saleem. 2013. Characterizations of Ideals in Intermediate C-Rings A(X) via the A-Compactifications of X. International Journal of Mathematics and Mathematical Sciences،Vol. 2013, no. 2013, pp.1-6.
https://search.emarefa.net/detail/BIM-486954
Modern Language Association (MLA)
Sack, Joshua& Watson, Saleem. Characterizations of Ideals in Intermediate C-Rings A(X) via the A-Compactifications of X. International Journal of Mathematics and Mathematical Sciences No. 2013 (2013), pp.1-6.
https://search.emarefa.net/detail/BIM-486954
American Medical Association (AMA)
Sack, Joshua& Watson, Saleem. Characterizations of Ideals in Intermediate C-Rings A(X) via the A-Compactifications of X. International Journal of Mathematics and Mathematical Sciences. 2013. Vol. 2013, no. 2013, pp.1-6.
https://search.emarefa.net/detail/BIM-486954
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-486954