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

By Wei Wei, Y. Qiang, Jing Zhang. 2013

63 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/b2a438baff3c690774509e0cc30825e62e4c34fa

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