Representations of Locally Inverse *-Semigroups
Representations of Locally Inverse *-Semigroups
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局部逆*-半群的表示
DOI：
10.1142/s0218196796000295
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
Hiroaki Yokoyama
中科院分区：
文献类型：
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作者：
T. Imaoka;Isamu Inata;Hiroaki Yokoyama
第一作者得到了广义逆 *-半群的Preston-Vagner表示定理的一个推广。本文将他们的结果推广到局部逆 *-半群。首先，通过引入π-集的概念（与[7]中的概念略有不同），构造了π-集上的π-对称局部逆 *-半群，并证明了任何局部逆 *-半群都可以嵌入到π-集上的π-对称局部逆半群中直到 *-同构.此外，我们还得到了局部逆 *-半群的圈积也是局部逆 *-半群。
The first author obtained a generalization of Preston-Vagner Representation Theorem for generalized inverse *-semigroups. In this paper, we shall generalize their results for locally inverse *-semigroups. Firstly, by introducing a concept of a π-set (which is slightly different from the one in [7]), we shall construct the π-symmetric locally inverse *-semigroup on a π-set, and show that any locally inverse *-semigroup can be embedded up to *-isomorphism in the π-symmetric locally inverse semigroup on a π-set. Moreover, we shall obtain that the wreath product of locally inverse *-semigroups is also a locally inverse *-semigroup.