半群CI(n,r)的极大(完全)独立子半群

Maximal (Completely) Isolated Subsemigroups of Semigroup CI(n,r)

摘要: 设I_n和S_n分别是有限集X_n={1,2,…,n}上的对称逆半群和对称群。对0≤r≤n−1，令I(n,r)={α∈I_n:|im(α)|≤r}，则I(n,r)是对称逆半群I_n的双边理想。记C_n=，其中g=(12…n)，称C_n为X_n上的循环群。通过分析半群CI(n,r)=I(n,r)∪C_n的格林关系及生成关系，获得了半群CI(n,r)的(完全)独立子半群的完全分类。进一步，证明了半群CI(n,r)的极大独立子半群与极大完全独立子半群是一致的。

Abstract: Let I_n and S_n be symmetric inverse semigroup and symmetric group on the finite set X_n={1,2,…,n}, respectively. For 0≤r≤n−1, put I(n,r)={α∈I_n:|im(α)|≤r}, then the I(n,r) is a two-sided ideal of symmetric inverse semigroup I_n. Denote C_n=, where there is g=(12…n), say that C_n is a circle group on X_n. By analyzing the Green’s relation and generative relation of the semigroup CI(n,r)=I(n,r)∪C_n, the complete classification of the (completely) isolated subsemigroups of CI(n,r) is obtained. Further, the coincide of maximal isolated subsemigroups and maximal completely isolated subsemigroups of semigroups CI(n,r) be proved.