Heyting代数中同余关系的简化

Simplification of congruence relation in Heyting algebra

给出了Heyting代数中同余关系的一种简单定义,这种定义并不改变全体滤子和全体同余关系之间的一一对应性,并且借助滤子证明了这种定义是Heyting代数作为泛代数的同余关系的简化。最后证明了全体滤子之集作为完备格同构于全体同余关系之集。

A simple definition for congruence relations in Heyting algebra is introduced. This definition does not change the one-one correspondence between all congruence relations and all filters. It is the simplification of congruence relations in Heyt- ing algebra as universal algebra. It is shown that the set of all congruence relations is isomorphic to the set of all filters as com- plete lattices.