Degree Type

Dissertation

Date of Award

1993

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

J. D. H. Smith

Abstract

The first of two results is a 1-1-correspondence between isomorphism classes of finite-dimensional vector lattices and finite rooted unlabelled trees. Thus the problem of counting isomorphism classes of finite-dimensional vector lattices reduces to the well-known combinatorial problem of counting these trees. The correspondence is used to identify the class of congruence lattices of finite-dimensional vector lattices as the class of finite dual relative Stone algebras, in partial answer to a question posed by Birkhoff. The next result constructs the lattice of congruences of a finite-dimensional vector lattice, via an algorithm, using the geometry of the positive cone.

DOI

https://doi.org/10.31274/rtd-180813-9721

Publisher

Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/

Copyright Owner

Michael Frederick Hobart

Language

en

Proquest ID

AAI9321165

File Format

application/pdf

File Size

34 pages

Included in

Mathematics Commons

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