幂等MV-代数

Idempotent MV-algebras

设M是一个MV-代数,如果M是Artinian幂等的,则M是有限个极小理想的直和.对于有限MV-代数M,M是幂等的当且仅当存在正整数n,使得|M|=2n;当且仅当M同构于MV-代数2X,其中X是由n个元素组成的集合.

Let M be an MV-algebra. If M is Artinian and idempotent, then M is a sum of finite many minimal ideals of M For a finite MV-algebra M, M is idempotent if and only if /M/ =2^x for some positive integer n; if and only if it is isomorphic to MV-algebra 2^x for some nonempty set X with /X/=n.