Geodesic
An interesting class of ideals in subalgebras of $C(X)$ containing $C^*(X)$
Commentationes Mathematicae Universitatis Carolinae, Tome 48 (2007) no. 2, pp. 273-280

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In the present paper we give a duality between a special type of ideals of subalgebras of $C(X)$ containing $C^*(X)$ and $z$-filters of $\beta X$ by generalization of the notion $z$-ideal of $C(X)$. We also use it to establish some intersecting properties of prime ideals lying between $C^*(X)$ and $C(X)$. For instance we may mention that such an ideal becomes prime if and only if it contains a prime ideal. Another interesting one is that for such an ideal the residue class ring is totally ordered if and only if it is prime.
Classification : 54C30, 54C35, 54C40, 54D35
Keywords: Stone-Čech compactification; rings of continuous functions; maximal ideals; $z^{\beta}_A$-ideals 
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     title = {An interesting class of ideals in subalgebras of $C(X)$ containing $C^*(X)$},
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Acharyya, Sudip Kumar; De, Dibyendu. An interesting class of ideals in subalgebras of $C(X)$ containing $C^*(X)$. Commentationes Mathematicae Universitatis Carolinae, Tome 48 (2007) no. 2, pp. 273-280. http://geodesic.mathdoc.fr/item/CMUC_2007__48_2_a8/