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Dimension in algebraic frames, II: Applications to frames of ideals in $C (X)$

Jorge Martinez; Eric R. Zenk — 2005

Commentationes Mathematicae Universitatis Carolinae

This paper continues the investigation into Krull-style dimensions in algebraic frames. Let $L$ be an algebraic frame. $dim (L)$ is the supremum of the lengths $k$ of sequences $p_{0} < p_{1} < \dots < p_{k}$ of (proper) prime elements of $L$ . Recently, Th. Coquand, H. Lombardi and M.-F. Roy have formulated a characterization which describes the dimension of $L$ in terms of the dimensions of certain boundary quotients of $L$ . This paper gives a purely frame-theoretic proof of this result, at once generalizing it to frames which are not necessarily...

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Dimension in algebraic frames, II: Applications to frames of ideals in C ( X )

Dimension in algebraic frames, II: Applications to frames of ideals in $C (X)$