Degree Type

Dissertation

Date of Award

2006

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Roger D. Maddux

Abstract

Relation algebras are abstractions of collections of binary relations under the operations of union, intersection, complementation, relational composition, inversion, and identity. A relation algebra is called representable if it is isomorphic to such a collection of relations. An algebra is called weakly representable if it is isomorphic to a collection of relations not necessarily closed under union and complementation. We consider weak representations over finite sets and note a connection between weak representations and relativizations. We also consider the question from Bjarni Jonsson's 1959 paper, whether the class of weakly representable relation algebras forms a variety. We show that it is, provided that a certain embedding condition obtains. Remaining open questions are collected in the concluding remarks.

DOI

https://doi.org/10.31274/rtd-180813-15417

Publisher

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

Copyright Owner

Jeremy F. Alm

Language

en

Proquest ID

AAI3217250

File Format

application/pdf

File Size

54 pages

Included in

Mathematics Commons

Share

COinS