自由幺半群的一族极大自由幺子半群

A family maximal free submonoids of the free monoid X^＊

设X*是由字母表X生成的自由幺半群,{B1,B2}是X的任意2—划分,C=B2∪B1XN,N≥1,文[1][2]中证明了C*是自由幺半群X*的幺子半群。以X*为顶点集构造了一个语言图,利用它证明了:对N≥1,C=B2∪XNB1,幺半群C*也是自由幺半群X*的一族极大自由幺子半群.

Let X^＊ be the free monoid generated by an alphabet X. Let {B1 ,B2} be an arbitrary twopartition on X and C =B2 ∪B1X^N,where N≥1. In [ 1 ] [2], monoid C^＊ is shown to be maximal free submonoids of the free monoid. This paper constructs a language diagram with X^＊ as node set, and shows that monoid C^＊, where C = B2 ∪ X^NB1, N ≥ 1, is also maximal free submonoids of the free monoid.