A Bijection between Lattice-Valued Filters and Lattice-Valued Congruences in Residuated Lattices

الملخص EN

The aim of this paper is to study relations between lattice-valued filters and lattice-valued congruences in residuated lattices.

We introduce a new definition of congruences which just depends on the meet ∧ and the residuum →.

Then it is shown that each of these congruences is automatically a universal-algebra-congruence.

Also, lattice-valued filters and lattice-valued congruences are studied, and it is shown that there is a one-to-one correspondence between the set of all (lattice-valued) filters and the set of all (lattice-valued) congruences.