半群X＊的一族极大自由幺子半群的推广

Extension of a family maximal free submonoids of the semigroup 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,A=B2∪E,其中E=B1XN(B02B1∪B2B1∪B22B1∪…∪BM2-1B1∪BM2X),N≥0,M≥0.对N=0,文[1]证明了幺半群A*是自由幺半群X*的极大自由幺子半群。利用文[2]的结果证明了对N≥2,幺半群A*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, {B1 ,B2} be an arbitrary two-parti- tion on X,and A=B2UE,where E=B1XN（B02B1UB2B1UB22B1U…UB2M-1B1UB2MX）,N≥0,M≥0.In [ 1 ] , monoid A ＊ are shown to be maximal free submonoids of the free monoid, where N = 0. In this paper, we have showed that monoid A ＊ are also maximal free submonoids of the monoid X＊ ,where N≥2.