Principal Congruence on Boolean Lattices
Cao Fa-sheng · Journal of Sichuan Normal University · 2012
Congruences,which are closely related to quotient algebras,play an important role in algebra theory.The researchers study the lattices which are the sets of all congruences with subsumption relation.Principal congruences as special congruences are concerned.The indiscernible index set for elements of Boolean lattices is defined based on isomorphism representation of subdirect product on Boolean lattices,and the simple properties of them are discussed.Then equivalent characterization for principal congruence on Boolean lattices is obtained by the indiscernible index set for elements of Boolean lattices.Finally,the relationship of cardinal number of the indiscernible index set and principal congruence on finite Boolean lattices is studied.The construction methods for principal congruences on Boolean lattices are obtained.