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Congruences in residuated lattices

机译:剩余格中的同余

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The aim of this paper is to study congruences in residuated lattices. A congruence in an algebra in a universal sense is an equivalence which preserves all the algebraic operations. In every residuated lattice (L, ???, ???, ???, ???), we show that an equivalence is a universal congruence, iff it preserves both ??? and ???, iff it is respect to both ??? and ???. If the residuated lattice is divisible, then an equivalence is a universal congruence iff it preserves both ??? and ???. Further, if the residuated lattice is an MV-algebra, then an equivalence is a universal congruence iff it just preserves ???. A potential mistake in [8] is pointed out.
机译:本文的目的是研究剩余格中的全等。通用意义上的代数相等是保留所有代数运算的等价关系。在每个剩余的点阵中(L,???,???,???,???),我们证明等价项是一个通用的等价项,只要它保留了两个等价项即可。和???,如果它尊重两者???和 ???。如果剩余格是可分割的,则等价是一个通用的等价性,前提是它保留了两个等价性。和 ???。此外,如果剩余的格是MV代数,则等价是仅保留???的通用等价性。在[8]中指出了一个潜在的错误。

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