Representations of Locally Inverse *-Subsemigroups II
Representations of Locally Inverse *-Subsemigroups II
复制标题
局部逆*-子半群 II 的表示
DOI：
10.1007/pl00005927
复制
发表时间：
1997
期刊：
影响因子：
0.7
通讯作者：
M. Katsura
中科院分区：
文献类型：
--
作者：
T. Imaoka;M. Katsura
第一作者推广了广义逆*-半群的Preston-Vagner表示定理。在本文中，我们将它们的结果推广到局部逆*-半群。首先，通过引入π-集合的概念（与[7]中的概念稍有不同），构造π-集合上的π-对称局部逆*-半群，并证明任一π-集合上的π-对称局部逆*-半群可以嵌入到π-集合上的*-同构。进一步证明了局部逆*-半群的环积也是一个局部逆*-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.