| 正则半群上的强同余 |
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| 引用本文： | 李艳,喻秉钧.正则半群上的强同余[J].四川师范大学学报(自然科学版),2007,30(6):708-713. |
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| 作者姓名： | 李艳 喻秉钧 |
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| 作者单位： | 1. 仰恩大学,数学系,福建,泉州,302614
2. 四川师范大学,数学与软件科学学院,四川,成都,610066 |
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| 摘 要： | 证明了正则半群上的所有强同余构成该半群同余格的完备子格,刻画了与强同余对应的核-迹同余对-强同余对及其相互关系,由此给出正则半群上任一强同余的结构,并证明了强同余格和强同余对的集合之间一一对应.
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| 关 键 词： | 正则半群 强同余 强同余对 |
| 文章编号： | 1000-8395（2007）06-0708-06 |
| 收稿时间： | 2006-03-01 |
| 修稿时间： | 2006年3月1日 |
Strong Congruences on Regular Semigroups |
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| LI Yan,YU Bing-jun.Strong Congruences on Regular Semigroups[J].Journal of Sichuan Normal University(Natural Science),2007,30(6):708-713. |
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| Authors: | LI Yan YU Bing-jun |
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| Abstract: | The aim of this paper is to study inverse semigroup congruences on an arbitrary regular semigroup S called strong congruence.It is proved that the set SC(S) of all strong congrunces on S forms a complete sublattice of the congruence lattice C(S) of S.Furthermore,the kernel-trace congrunce pairs corresponding to the strong congruences,i.e.,strong congrunce pairs as well as the relationship between them are characterized.By using these,a structure theorem for strong congruences on S is given.It is also proved that there exists a bijection between the lattice SC(S) and the set of all strong congrunce pairs of the regular semigroup S. |
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| Keywords: | Regular semigroups Strong congruences Strong congruence pairs |
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