剩余格的TL-滤子与TL-同余关系

TL-filters and TL-congruences of residuated lattices

将有界格上的t-模T应用于剩余格的滤子和同余上,提出了剩余格的TL-滤子与TL-同余关系。首先,研究TL-滤子与TL-同余的性质与一些等价刻画。得到了TL-滤子的集合与TL-同余关系的集合是同构的。最后研究了剩余格的商结构与同态定理,这些理论在其他逻辑代数系统中依然成立。

t-norm T of bounded lattices is applied to filters and congruences in residuated lattices,and the concept of TL-filters and TL-congruences of a residuated lattice are introduced.Their properties and some equivalent characterizations are derived.We prove that there is a correspondent bijection between the set of all TL-filters of a residuated lattice and the set of all TL-congruences in that residuated lattice.Finally,quotient residuated lattices and homomorphism theorem are derived.These results and methods still hold in other logical algebraic structures.