半群I_(n,r)的极大(完全)独立子半群

MAXIMAL(COMPLETELY)ISOLATEDSUBSEMIGROUPS OF SEMGROUP I_(n,r)

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,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.对0≤r≤n-1,再令I_(n,r)=S_(n)UI(n,r),则I_(n,r)是对称逆半群I_(n)的子半群.为了研究半群I_(n,r)的极大(完全)独立子半群的完全分类,本文分析了半群I_(n,r)的格林关系及生成关系.首先,获得了半群I_(n,r)的(完全)独立子半群的完全分类;其次,确定了半群I_(n,r)的极大(完全)独立子半群的完全分类;最后,证明了半群I_(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 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,put I_(n,r)={α∈I_(n):imα≤r},then the I(n,r) are the two-sided ideals of I_(n).For 0≤r≤n-1,put I_(n,r)=S_(n)∪I(n,r),then the I(n,r) are the subsemigroups of I_(n).In order to study complete classification of the maximal(completely)isolated subsemigroups of I_(n,r),the Green′s relation and generation of I_(n,r) are analyzed.Firstly,the complete classification of the(completely)isolated subsemigroups of I_(n,r) is obtained.Secondly,the complete classification of the maximal(completely)isolated subsemigroups of I_(n,r) is determined.Finally,the coincide of maximal isolated subsemigroups and maximal completely isolated subscemigroups of I_(n,r) be proved.