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- Title
Distribution of Prime Ideals in Subalgebras of C (X).
- Authors
De, Dibyendu
- Abstract
Let X be a completely regular Hausdorff topological space and ∑(X) the class of all subalgebras of C(X) containing C*(X). Byun and Watson published a paper in Topology and its Application in 1991, some of whose results had been corrected in the Doctoral Dissertation of present author and reproved recently by Acharyya and Bose in a paper of Topology and its Application. In the present article we prove that the class of all prime ideals in an intermediate ring A(X) that lie between a non-maximal prime ideal and the unique maximal ideal extending it constitutes a Dedekind complete chain with atleast 2/¹ many members. A special case of this result with A(X) = C(X) (respectively C* (X)) is already covered in Gillman-Jerison text. From this it follows that if A (X) ≄ C(X) then there are atleast 2/¹ many non-maximal prime ideals in A(X). This generalizes a well known fact established by Gillman and Henriksen longtime ago and also sharpens a corresponding recent result of Acharyya and Bose.
- Subjects
PRIME ideals; DISTRIBUTION (Probability theory); ALGEBRA; TOPOLOGY; MAXIMAL ideals; PRIME numbers
- Publication
Southeast Asian Bulletin of Mathematics, 2016, Vol 40, Issue 6, p815
- ISSN
0129-2021
- Publication type
Article