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Logic Journal of IGPL Advance Access published online on July 25, 2007
Logic Journal of IGPL, doi:10.1093/jigpal/jzm014
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© The Author, 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Congruences on Dynamic Algebras

Sandra Marques Pinto

Departamento de Matemática, Universidade de Coimbra, Portugal. E-mail: sandra{at}mat.uc.pt

Teresa Oliveira-Martins

Departamento de Matemática, Universidade de Coimbra, Portugal. E-mail: meresa{at}mat.uc.pt

M. Céu Pinto

Departamento de Matemática, Universidade de Coimbra, Portugal. E-mail: pinto{at}mat.uc.pt


  Abstract

The lattice CongFormula of all dynamic congruences on a given dynamic algebra Formula is presented. Whenever Formula is separable with zero we define dynamic ideal on Formula, given rise to the lattice IdeFormula. The notions of kernel of a dynamic congruence and the congruence generated by a dynamic ideal are introduced to describe a Galois connection between CongFormula and IdeFormula. We study conditions under which a dynamic congruence is determined by its kernel.

Key Words: Boolean algebra with operators • dynamic algebra • dynamic congruence • dynamic ideal • Galois connection

Received for publication 5 December 2005. Revision received 24 February 2006.
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