半群Pn,r的极大(正则)子半群
The Maximal (Regular) Subsemigroups of Semigroup Pn,r
摘要: 设S
n和P
n分别是X
n={1,2,…,n}上的对称群和部分变换半群。对0≤r≤n，令P(n,r)={α∈P
n:|im(α)≤r}，则P(n,r)是部分变换半群P
n的子半群。对0≤r≤n-1，考虑半群P
n,r=P
n,r∪S
n的极大(正则)子半群。通过对半群P
n,r格林关系的分析进一步，获得了半群P
n,r的极大子半群和极大正则子半群是一致的。
Abstract:
Let Sn and Pn be symmetric group and partial transformation semigroup on Xn={1,2,…,n}, respectively. For 0≤r≤n, put P(n,r)={α∈Pn:|im(α)≤r}, then the set P(n,r) are the subsemigroups of . For 0≤r≤n-1. In this paper, the maximal (regular) subsemigroups of the semigroup Pn,r=Pn,r∪Sn has been considered. In addition, by analyzing the Green’s relations, this paper proved that the maximal subsemigroups and the maximal regular subsemigroups of Pn,r coincide.
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