| 弱逆半群上最大幂等元分离同余和群同余 |
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| 引用本文： | 喻秉钧,廖群英,余时伟. 弱逆半群上最大幂等元分离同余和群同余[J]. 四川师范大学学报(自然科学版), 2001, 24(3): 219-223 |
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| 作者姓名： | 喻秉钧 廖群英 余时伟 |
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| 作者单位： | 1. 四川师范大学数学系
2. 电子科技大学应用数学系 |
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| 基金项目： | 国家自然科学基金(19671063)和四川省教委重点科研基金资助项目 |
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| 摘 要： | 刻画了弱逆半群S上的最大幂等元分离同余和最小群同余，在此基础上，证明了S的群同余格与S的由主元所组成的逆半群I（S）的群同余格完备格同构；进而，证明了I（S）的群同余格是S的同余格的格同态像。
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| 关 键 词： | 弱逆半群 群同余 最大幂等元分离同余 格同态 完备格同构 同余格 |
| 文章编号： | 1001-8395（2001）03-0219-05 |
| 修稿时间： | 2001-02-28 |
The Greatest Idempotent-separating Congruence and Group Congruences on a Weakly Inverse Semigroup |
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| YU Bing-jun,LIAO Qun-ying,YU Shi-wei. The Greatest Idempotent-separating Congruence and Group Congruences on a Weakly Inverse Semigroup[J]. Journal of Sichuan Normal University(Natural Science), 2001, 24(3): 219-223 |
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| Authors: | YU Bing-jun LIAO Qun-ying YU Shi-wei |
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| Affiliation: | YU Bing jun 1,YU Shi wei 2,LIAO Qun ying 1 |
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| Abstract: | In this paper, the greatest idempotent separating congruence and the minimum group congruence on a weakly inverse semigroup S are characterized. It is proved therefore that the lattice of group congruences on S is complete lattice isomorphic to the lattice of group congruences on I(S) , the inverse subsemigroup of principal elements of S . Moreover, the lattice of group congruences of S is also a lattice homomorphic image of the lattice of all congruences of S . |
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| Keywords: | Weakly inverse semigroup Group congruence Greatest idempotent-separating congruence Lattice Lattice homomorphism Complete lattice isomorphism |
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