AN EQUIVALENT DEFINITION OF COMPLETE CONGRUENCE RELATIONS
Yu Zhang · 1999
In this paper,we define the chain transitive relation and obtain the following results:(1) Let L be a complete lattice.Then θ is a complete congruence relation iff θ is a chain transitive congruence relation;(2) If θ is a chain transitive relation,then θ is a complete congruence relation iff θ satisfies the substitution property.From these results,we can define the complete congruence relation θ as the chain transitive relation θ with the substitution property.