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

Jorge Martinez, Eric R. Zenk (2005)

Commentationes Mathematicae Universitatis Carolinae

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This paper continues the investigation into Krull-style dimensions in algebraic frames. Let $L$ be an algebraic frame. $dim\left(L\right)$ is the supremum of the lengths $k$ of sequences ${p}_{0}<{p}_{1}<\cdots <{p}_{k}$ 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...