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

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  • Wei Wei
  • Yan Qiang
  • Jing Zhang

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.

Suggested Citation

  • Wei Wei & Yan Qiang & Jing Zhang, 2013. "A Bijection between Lattice-Valued Filters and Lattice-Valued Congruences in Residuated Lattices," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-6, July.
    • Handle: RePEc:hin:jnlmpe:908623
    DOI: 10.1155/2013/908623
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