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
Copyright Date
2006
Language
en
Proquest ID
AAI3217250
File Format
application/pdf
File Size
54 pages
Recommended Citation
Alm, Jeremy F., "Weak representation theory in the calculus of relations " (2006). Retrospective Theses and Dissertations. 1795.
https://lib.dr.iastate.edu/rtd/1795
