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

Wei Wei, Yan Qiang and Jing Zhang

Mathematical Problems in Engineering, 2013, vol. 2013, 1-6

Abstract:

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.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:908623

DOI: 10.1155/2013/908623

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