Eric Richard Zenk

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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. Lom-bardi and M.-F. Roy have formulated a characterization which describes the dimension of L in terms of(More)
Dedicated to the memory of our dear friend and colleague, Mel Henriksen. Abstract. We show that every completely regular frame has a P-frame re ‡ection. The proof is straightforward in the case of a Lindelöf frame, but more complicated in the general case. The chief obstacle to a simple proof is the important fact that a quotient of a P-frame need not be a(More)
This paper is divided into two parts. First, the assembly NL of a frame L and the subframe BL of blocks – that is, the nuclei on L arising as a join of open nuclei – are used to describe the coreflection in fit frames: the pullback QL of BL over the natural embedding cL of L in the assembly is the first step in a transfinite nesting of subframes of L, the(More)
This article discusses the basic categorical algebra for categories of partial frames. Categories of partial frames are labelled by subset selectors that indicate which joins exist. Constructions for limits, colimits, and free functors connecting various categories of partial frames are given. Examples of partial frame categories are given. Subset selectors(More)
The least element 0 of a finite meet semi-distributive lattice is a meet of meet-prime elements. We investigate conditions under which the least element of an algebraic, meet semi-distributive lattice is a (complete) meet of meet-prime elements. For example, this is true if the lattice has only countably many compact elements, or if |L| < 2 ℵ 0 , or if L is(More)
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