| 完全0-单半群的同态像和某些同余 |
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| 引用本文： | 张润石,李艳,喻秉钧.完全0-单半群的同态像和某些同余[J].四川师范大学学报(自然科学版),2007,30(2):146-150. |
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| 作者姓名： | 张润石 李艳 喻秉钧 |
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| 作者单位： | 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： | 证明了完全0-单半群的真同态像仍完全0-单，给出了其结构；刻画了完全0-单半群的最大真同余及其商；给出了有0和本原幂等元的半群S无同余的充要条件；讨论了完全0-单半群上的幂等元纯同余，幂等元分离同余及其同态像；给出了完全0-单半群存在0-群同余的充要条件并刻画了其0-群同态像．
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| 关 键 词： | 完全0-单半群 真同余 无同余 0-限制矩形带 幂等元纯同余 幂等元分离同余 0-群同余 |
| 文章编号： | 1001-8395（2007）02-0146-05 |
| 收稿时间： | 2005-11-14 |
| 修稿时间： | 2005年11月14 |
The Homomorphic Images of a Completely 0-simple Semigroup and Some Congruences on It |
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| ZHANG Run-shi,LI Yan,YU Bin-jun.The Homomorphic Images of a Completely 0-simple Semigroup and Some Congruences on It[J].Journal of Sichuan Normal University(Natural Science),2007,30(2):146-150. |
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| Authors: | ZHANG Run-shi LI Yan YU Bin-jun |
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| Institution: | College of Mathematics and Software Science, Sichuan Nbrrnal University, Chengdu 610066, Sichuan |
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| Abstract: | In this paper, it is proved that proper homomorphic images of a completely 0-simple semigroup are also completely 0- simple. The structure of the images is described. The maximum proper congruence on a completely 0-simple semigroup and its image are characterized. The sufficient and necessary condition for a semigroup with 0 and primitive idempotent to be congruence-free is given. Idempotet-pure and idempotent-separating congruences on a completely 0-simple semigroup and their images are discussed. The sufficient and necessary condition for a completely 0-simple semigroup to have 0-group congruence is given and the 0-group homomorphic images are characterized. |
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| Keywords: | Completely 0-simple semigroup Pproper congruence Congruence-free 0-restricted rectangular band Idempotent pure-congruence Idempotent-separating congruence 0-group congruence |
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