Abstract: In residuated lattices, a definition of congruence relations is introduced depending on the meet opration[∧]and the implication operation[→], which simplifies the forms of congruence relations in sense of universal algebras. It is shown that all this kind of congruence relations are still one-to-one corresponding to all filters and indeed such a correpondence is an isomorphism between related complete lattices.

Key words: residuated lattice, congruence relation, filter

摘要： 在剩余格中定义了一种只依赖于交运算和蕴含算子的同余关系，简化了[L]作为泛代数的同余关系的表达式，证明了这种同余关系和滤子之间仍然是一一对应的，并且这种对应关系是相应的完备格之间的一个同构。

关键词: 剩余格, 同余关系, 滤子