Orthodox Transversals of Regular Semigroups
Orthodox Transversals of Regular Semigroups
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DOI：
10.1142/s0218196701000541
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发表时间：
2001-04
期刊：
影响因子：
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通讯作者：
J. F. Chen;Y. Cuo
中科院分区：
文献类型：
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作者：
J. F. Chen;Y. Cuo
正统断面是由第一作者作为逆断面的推广引入的[Comm.代数27(9)(1999)，第4275-4288页]。我们在这本笔记中的目的之一是考虑东正教横断面的一般情况。主要结果是关于具有纯正断面的正则半群的两个分支集I和Λ。我们证明了Ī和分别由I和Λ生成的半带是带。本文还给出了纯正半群性质的一些有趣的推广；本文的另一个目的是给出一些例子，说明具有纯正断面的正则半群类适当地包括具有逆断面的正则半群类以及纯正半群类。
Orthodox transversals were introduced by the first author as a generalization of inverse transversals [Comm. Algebra 27(9) (1999), pp. 4275–4288]. One of our aims in this note is to consider the general case of orthodox transversals. The main results are on the sets I and Λ, two components of regular semigroups with orthodox transversals. We prove that the semibands Ī and generated by I and Λ respectively are bands. Also somewhat interesting generalizations of properties on orthodox semigroups are given; another aim in this note is to give some examples illustrating the situations that the class of regular semigroups with orthodox transversals properly includes the class of regular semigroups with inverse transversals as well as the class of orthodox semigroups.