Filters on positive cones of lattice-ordered groups
Tumpa Bhattacharyya · OhioLink ETD Center (Ohio Library and Information Network) · 2011
In a recent article "Bazzoni's Conjecture" the authors used lattice-theoretic techniques to positively answer a conjecture of Bazzoni's regarding Pr¨ fer domains.Suppose is an ℓ-group and is a filter on + .Recall that is a principal filter if it is of the form { ∈ + : ≤ } for some ∈ + .We say that is a cold filter if for all ∈ ( ), the filter(i.e. the interval) on ( / ) + defined by = { + : ∈ } has a minimum.If every filter on + is principal(resp.cold)then we say that the group is principally-filtered(resp.coldfiltered) ℓ-group.In this dissertation we expand on the ideas of cold filters and characterize cold-filtered ℓ-groups.iii ACKNOWLEDGMENTS (i) I would heartily like to thank my advisor Dr. Warren Wm.McGovern for believing in me and motivating me to do this research.There was a point in time when I had no results.But thanks to