Heyting代数中同余关系的简化

摘要

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 Heyting algebra as universal algebra. It is shown that the set of all congruence relations is isomorphic to the set of all filters as complete lattices.