A bijection between lattice-valued filters and lattice-valued congruences in residuated lattices (Q474252)
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scientific article; zbMATH DE number 6372714
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A bijection between lattice-valued filters and lattice-valued congruences in residuated lattices |
scientific article; zbMATH DE number 6372714 |
Statements
A bijection between lattice-valued filters and lattice-valued congruences in residuated lattices (English)
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24 November 2014
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Summary: 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 \(\wedge\) and the residuum \(\to\). 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.
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