ON THE PARTITION MONOID AND SOME RELATED SEMIGROUPS
ON THE PARTITION MONOID AND SOME RELATED SEMIGROUPS
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关于分区幺半群和一些相关的半群
DOI：
10.1017/s0004972710001851
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发表时间：
2010
影响因子：
0.7
通讯作者：
K. Lau
中科院分区：
文献类型：
--
作者：
D. Fitzgerald;K. Lau
摘要划分么半群是 *-正则半群的一个突出的自然例子。我们发现一个伽罗瓦连接的元素之间的分区幺半群和二元关系，并用它来表明，分区幺半群包含副本的变换半群和对称和双对称逆半群的基础集。我们的特点是整除前序和自然秩序的（直）分区幺半群，使用某些图形结构与每个元素。这给出了绿色关系的更简单的表征。我们还得到了变换半群上自然序的一个新的解释。这些结果也被用来描述直的和扭曲的分割幺半群和Brauer幺半群的理想格。
Abstract The partition monoid is a salient natural example of a *-regular semigroup. We find a Galois connection between elements of the partition monoid and binary relations, and use it to show that the partition monoid contains copies of the semigroup of transformations and the symmetric and dual-symmetric inverse semigroups on the underlying set. We characterize the divisibility preorders and the natural order on the (straight) partition monoid, using certain graphical structures associated with each element. This gives a simpler characterization of Green’s relations. We also derive a new interpretation of the natural order on the transformation semigroup. The results are also used to describe the ideal lattices of the straight and twisted partition monoids and the Brauer monoid.