| 半群W(n,r)的极大(正则)子半群 |
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| 引用本文： | 罗永贵. 半群W(n,r)的极大(正则)子半群[J]. 山东大学学报(理学版), 2017, 52(10): 7-11. DOI: 10.6040/j.issn.1671-9352.0.2016.471 |
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| 作者姓名： | 罗永贵 |
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| 作者单位： | 贵州师范大学数学科学学院, 贵州 贵阳 550001 |
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| 基金项目： | 贵州省科学技术基金资助项目(黔科合LH字(2014)7056号) |
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| 摘 要： | 设自然数n≥3, RWn是有限链［n］上的正则保序且压缩奇异变换半群。对任意的r(1≤r≤n-1), 记W(n,r)={α∈RWn:|Im(α)|≤r}为半群RWn的双边理想。通过对秩为r的元素和格林关系的分析, 获得了半群W(n,r)的极大(正则)子半群的完全分类。
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| 关 键 词： | 奇异变换半群 完全分类 正则压缩 保序 极大(正则)子半群 |
| 收稿时间： | 2016-10-20 |
Maximal(regular)subsemigroups of the semigroup W(n,r) |
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| LUO Yong-gui. Maximal(regular)subsemigroups of the semigroup W(n,r)[J]. Journal of Shandong University, 2017, 52(10): 7-11. DOI: 10.6040/j.issn.1671-9352.0.2016.471 |
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| Authors: | LUO Yong-gui |
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| Affiliation: | School of Mathematics Science, Guizhou Normal University, Guiyang 550001, Guizhou, China |
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| Abstract: | Let RWn be the semigroup of all regular order-preserving and compressing singular transformations on a finite-chain［n］ if n≥3, and let W(n,r)={α∈RWn:|Im(α)|≤r} be the two-sided ideal of the semigroup RWn for an arbitrary integer r accord with 1≤r≤n-1. By analyzing the elements of rank r and Greens relations, the classification of the maximal(regular)subsemigroup of the semigroup W(n,r) is completely obtained. |
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| Keywords: | regular compression order-preserving maximal(regular)subsemigroup singular transformation semigroup complete classification |
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