半群CI(n,r)的极大(完全)独立子半群

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

设In和Sn分别是有限集Xn={1,2,…,n}上的对称逆半群和对称群。对0≤r≤n−1,令I(n,r)={α∈In:|im(α)|≤r},则I(n,r)是对称逆半群In的双边理想。记Cn=,其中g=(12…n),称Cn为Xn上的循环群。通过分析半群CI(n,r)=I(n,r)∪Cn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。

Let In and Sn be symmetric inverse semigroup and symmetric group on the finite set Xn={1,2,…,n}, respectively. For 0≤r≤n−1, put I(n,r)={α∈In:|im(α)|≤r}, then the I(n,r) is a two-sided ideal of symmetric inverse semigroup In. Denote Cn=, where there is g=(12…n), say that Cn is a circle group on Xn. By analyzing the Green’s relation and generative relation of the semigroup CI(n,r)=I(n,r)∪Cn, 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.