A NEW CONSTRUCTION FOR REGULAR SEMIGROUPS WITH QUASI-IDEAL ORTHODOX TRANSVERSALS
A NEW CONSTRUCTION FOR REGULAR SEMIGROUPS WITH QUASI-IDEAL ORTHODOX TRANSVERSALS
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DOI：
10.1017/s1446788708000566
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发表时间：
2009-04
影响因子：
0.7
通讯作者：
Xiangjun Kong;X. Zhao
中科院分区：
文献类型：
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作者：
Xiangjun Kong;X. Zhao
在具有纯正断面的正则半群中，利用绿色关系定义了两个集合R和L，并给出了它们是子半群的充要条件。利用R和L，得到了纯正断面是拟理想的几个等价条件。最后，利用两个纯正半群R和L给出了具有拟理想纯正断面的正则半群的一个结构定理。
Abstract In any regular semigroup with an orthodox transversal, we define two sets R and L using Green’s relations and give necessary and sufficient conditions for them to be subsemigroups. By using R and L, some equivalent conditions for an orthodox transversal to be a quasi-ideal are obtained. Finally, we give a structure theorem for regular semigroups with quasi-ideal orthodox transversals by two orthodox semigroups R and L.