The results that the strongly ordered congruences are the strongly regular congruences and that the converses are not true are proved.

What subsets of an ordered semigroup S can serve as a congruence class of certain regular congruence on S is still an open problem to be solved.

This paper first introduces the concepts of regular P-congruences and partial kernel normal system on S(P),then gives the regular P-congruences on S(P)an abstract characterization by means of the partial kernel normal system and a necessary and sufficient condition for a set B={B_i∶i∈I}of pairwise disjoint subsets of S(P)which is a partial kernel normal system in S(P)with P∩B_i as its C-set.

The basic properties of principal congruence relations of a MS-algebra are discussed.

In this paper, a congruence relations which is marked is introduced into N(2,2,0) algebra and a quotient algebra is established, and then the properties of natural homomorphic π are discussed.

In this paper the fundamental properties of principal congruence relations of a softalgebra are presented.

Methods of how to prove congruence relation;

Implication Filters and Congruence Relations in R 0 Algebras;

Study of congruence relation based on minimization theory of FA

Principal Congruences on Pseudocomplemented MS Algebras;

The Property of Congruence on Orthogonal Modular Lattice

This paper gives an equivalent characterization of De Morgan algebras by the operations of implication and negation and discusses the property of congruences induced by an implicit filter.