正则FI代数的MP滤子与同构基本定理

MP-filters and fundamental isomorphism theorem of regular FI-algebras

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。

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.