Congruences on Dynamic Algebras

Abstract

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