Congruences generated by filters
Jaromír Duda · Czech digital mathematics library · 1980
The main purpose of this paper is to charracterize the nodal filters in lattices (in up-directed mee^-semilattices) in terms of congruences.Thus J.C» Varlet s result, stated for implicative semilattices, is generalized for lattices and up-directed meet-semilattices.Further, we give the description of some well-known quotient lattices and quotient semilattices in more precise form.Finally, we compare lattice congruences, semilattice congruences and equivalence relations generated by filters of a lattice.