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Coherence classes of ideals of normal lattices with applications to $C(X)$

In: Mathematica Slovaca, vol. 63, no. 4
Themba Dube

Details:

Year, pages: 2013, 679 - 692
Keywords:
coherence class, normal lattice, rings of continuous functions
About article:
Given a topological space $X$, Jenkins and McKnight have shown how ideals of the ring $C(X)$ are partitioned into equivalence classes – called coherence classes – defined by declaring ideals to be equivalent if their pure parts are identical. In this paper we consider a similar partitioning of the lattice of ideals of a normal bounded distributive lattice. We then apply results obtained herein to augment some of those of Jenkins and McKnight. In particular, for Tychonoff spaces, new results include the following: (a) all members of any coherence class have the same annihilator, (b) every ideal is alone in its coherence class if and only if the space is a $P$-space.
How to cite:
ISO 690:
Dube, T. 2013. Coherence classes of ideals of normal lattices with applications to $C(X)$. In Mathematica Slovaca, vol. 63, no.4, pp. 679-692. 0139-9918. DOI: https://doi.org/10.2478/s12175-013-0128-z

APA:
Dube, T. (2013). Coherence classes of ideals of normal lattices with applications to $C(X)$. Mathematica Slovaca, 63(4), 679-692. 0139-9918. DOI: https://doi.org/10.2478/s12175-013-0128-z
About edition: