Congruence relations on double boolean algebras
by
Björn Vormbrock
student at TU Darmstadt

Double boolean algebras form the variety generated by the algebras of protoconcepts which are of importance in contextual logic. Every double boolean algebra contains two boolean algebras. We show that congruence relations on pure double boolean algebras may be characterized by pairs consisting of an ideal in one boolean algebra and a filter in the other. As every double boolean algebra contains a pure subalgebra, this result helps us to understand congruence relations on double boolean algebras in general. Moreover, we apply these results to contextual double boolean algebras and obtain a direct decomposition of the latter in simple contextual double boolean algebras.

Date received: February 8, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caht-24.