Vector lattices
Date
1993
Authors
Hobart, Michael
Major Professor
Advisor
J. D. H. Smith
Committee Member
Journal Title
Journal ISSN
Volume Title
Publisher
Altmetrics
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.
Series Number
Journal Issue
Is Version Of
Versions
Series
Academic or Administrative Unit
Type
dissertation
Comments
Rights Statement
Copyright
Fri Jan 01 00:00:00 UTC 1993