Abstract: The regular FI-algebras are built up on general sets by the implication operation uniquely. Both [BR0]-algebras and BL-algebras are examples of regular FI-algebras. This paper, by using the related ideas and methods in classical algebra, studies the MP-filters and isomorphism theorem of regular FI-algebras. Firstly, a concept of MP-filters is introduced and their basic properties are discussed. It gives the concrete structure of an MP-filter generated by a given subset. Secondly, the relations between MP-filters and congruence relations are discussed. Finally, the fundamental isomorphism theorems are established.

Key words: logic algebra, regular Fuzzy , Implication（FI）-algebra, Modus Ponens（MP）-filter, congruence relation, Fuzzy , Implication（FI）-homomorphism, fundamental theorem of isomorphism

摘要： 正则FI-代数是仅基于蕴涵算子在一般集合上建立的逻辑代数，它是[BR0]-代数和BL-代数的基础逻辑代数。基于经典代数的思想和方法，讨论了正则FI-代数的MP滤子与同构基本定理。引入正则FI-代数中MP滤子的概念，并讨论了其基本性质，给出了正则FI-代数中包含任意子集的最小MP滤子的构造方法；讨论了正则FI-代数的MP滤子和同余关系之间的内在联系；给出了正则FI-代数的同构基本定理。

关键词: 逻辑代数, 正则模糊蕴涵（FI）-代数, 分离规则（MP）滤子, 同余关系, 模糊蕴涵（FI）-同态, 同构基本定理