real ideals
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Positivity ◽  
2013 ◽  
Vol 18 (1) ◽  
pp. 1-8
Author(s):  
Sergio Albeverio ◽  
Rashidkhon A. Dadakhodjaev ◽  
Abdugafur A. Rakhimov


2010 ◽  
Vol 83 (2) ◽  
pp. 338-352 ◽  
Author(s):  
THEMBA DUBE

AbstractReal ideals of the ring ℜL of real-valued continuous functions on a completely regular frame L are characterized in terms of cozero elements, in the manner of the classical case of the rings C(X). As an application, we show that L is realcompact if and only if every free maximal ideal of ℜL is hyper-real—which is the precise translation of how Hewitt defined realcompact spaces, albeit under a different appellation. We also obtain a frame version of Mrówka’s theorem that characterizes realcompact spaces.





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