| 降序且保序的有限全变换半群 |
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| 引用本文： | 裴惠生,邹定宇,李连兵.降序且保序的有限全变换半群[J].信阳师范学院学报(自然科学版),2006,19(4):373-377,433. |
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| 作者姓名： | 裴惠生 邹定宇 李连兵 |
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| 作者单位： | 1. 信阳师范学院,数学与信息科学学院,河南,信阳,464000
2. 江苏工业学院,江苏,常州,213000 |
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| 基金项目： | Supported by NSF of Henan province(0511010200) |
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| 摘 要： | 设Jn为有限集X={1,2,…,n}上的全变换半群,Sn为Jn中所有奇异变换构成的子半群,记Sn-={f∈Sn:x∈X,f(x)≤x},Qn={f∈Jn:x,y∈X,x≤y f(x)≤f(y)},那么Sn-与Qn都是Tn的子半群,令Hn=S-n∩Qn,则Hn也是Jn的一个子半群,Hn的某些性质,诸如Green关系,Green星关系,秩和幂等秩都进行了研究,还证明了Hn是幂等元生成的,且可由J*中的n-1个幂等元生成.
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| 关 键 词： | 半群 变换 保序 降序 秩 幂等元 |
| 文章编号： | 1003-0972（2006）04-0373-05 |
| 收稿时间： | 2005-09-27 |
| 修稿时间： | 2005-09-27 |
On the Semigroup of Order-decreasing and Order-preserving Finite Full Transformations |
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| PEI Hui-sheng,ZOU Ding-yu,LI Lian-bing.On the Semigroup of Order-decreasing and Order-preserving Finite Full Transformations[J].Journal of Xinyang Teachers College(Natural Science Edition),2006,19(4):373-377,433. |
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| Authors: | PEI Hui-sheng ZOU Ding-yu LI Lian-bing |
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| Institution: | 1. College of Mathematics and Information Science, Xinyang Normal University, Xinyang 464000, China ; 2. Jiangsu Polytechnic University, Changzhou 213000, China |
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| Abstract: | Let Tn be the full transformation semigroup on the finite set X={1,2,...,n},Sn be the subsemigroup of all singular transformations in Tn.Denote S-n={f∈Sn:(A)x∈X,f(x)≤x},and On={f∈Tn:(A)x,y∈X,x≤y implies f(x)≤f(y)}.Then both S-n and On are subsemigroups of Tn.Let Hn=S-n∩On.Some properties for Hn,such as,Green's relations,Green's starred relations,rank and idempotent rank,are observed.Among other things,it is shown that Hn is idempotent-generated and that it is generated by n-1 idempotents in J*n-1. |
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| Keywords: | semigroup transformation order-preserving orderdecreasing rank idempotent |
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