Date of Award
Doctor of Philosophy
J. D. H. Smith
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.
Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/
Michael Frederick Hobart
Hobart, Michael Frederick, "Vector lattices " (1993). Retrospective Theses and Dissertations. 10448.