自由幺半群X^＊的两类极大自由幺子半群的推广

The extention of the two classes of 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。对N=1,2,文[1]证明了幺半群C*是自由幺半群X*的极大自由幺子半群。本文证明了:对N≥3,幺半群C*也是自由幺半群X*的极大自由幺子半群。

Let X^＊ be the free monoid generated by an alphabet X and { B1 ,B2 } be an arbitrary twopartition on X, C = B2∪B1X^N. In [ 1 ] monoid C^＊ is proved to be maximal free submonoids of the free monoid, where N = 1,2. In this paper, we prove that monoid C^＊ can also be maximal free submonoids of the free monoid X^＊ ,where N≥3.