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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 < < 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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