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| 半群PC(n,r)的幂等元秩 | |
| 引用本文： | 赵平,游泰杰,徐波. 半群PC(n,r)的幂等元秩[J]. 吉林大学学报(理学版), 2012, 50(1): 44-48 |
| 作者姓名： | 赵平 游泰杰 徐波 |
| 作者单位： | 1. 贵阳医学院 基础医学院, 贵阳 550004,2. 贵州师范大学 数学与计算机科学学院, 贵阳 550001 |
| 基金项目： | 贵州省科学技术基金(批准号:黔科合[2010]3174) |
| 摘 要： | 设PCn是有限链［n］上的降序且保序部分变换半群 . 对任意的3≤r≤n-1, 考虑半群PC(n,r)={α∈PCn: 〖JB(|〗Im(α)〖JB)|〗≤r} 的秩和幂等元秩, 证明了半群PC(n,r)是由秩为r的幂等元生成的, 并得到了PC(n,r)的秩和 幂等元秩均为∑〖DD(〗n〖〗k=r〖DD)〗〖JB((〗〖HL(1〗nk〖HL)〗〖JB))〗〖JB(( 〗〖HL(1〗k-1r-1〖HL)〗〖JB))〗. |
| 关 键 词： | 变换半群 降序 保序 幂等元秩 秩 |
| 收稿时间： | 2011-02-19 |
Idempotent Rank of Semigroup PC(n,r) |
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| ZHAO Ping,YOU Tai-jie,XU Bo. Idempotent Rank of Semigroup PC(n,r)[J]. Journal of Jilin University: Sci Ed, 2012, 50(1): 44-48 | |
| Authors: | ZHAO Ping YOU Tai-jie XU Bo |
| Affiliation: | 1. School of Basic Medicine, Guiyang Medical College, Guiyang 550004, China|2. School of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, China |
| Abstract: | Let PCn be the semigroup of all order-decreasing and order-preserving partial transformations on a finite-chain [n].For an arbitrary integer r such that 3≤r≤n-1,the rank and idempotent rank of the semigroup PC(n,r)={α∈PCn:︱Im(α)︱≤r} were studied.We showed that PC(n,r) is generated by idempotents of rank r.Furthermore,we obtained that the rank and idempotent rank of PC(n,r) are both equal to n∑k=r(nk)(k-1r-1). |
| Keywords: | transformation semigroup order-decreasing order-preserving idempotent rank rank |
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