| 半群O_n(k)的秩 |
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| 引用本文： | 张传军,赵平.半群O_n(k)的秩[J].数学的实践与认识,2014(9). |
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| 作者姓名： | 张传军 赵平 |
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| 作者单位： | 贵州省教育科学院;贵州师范大学; |
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| 基金项目： | 贵州省科学技术基金(黔科合J字[2013]2225号) |
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| 摘 要： | 设O_n是有限链n]上的保序变换半群.对任意1≤k≤n-1,研究半群O_n(k)={α∈O_n:(x∈n]x≤k→xα≤k}的秩和幂等元秩,证明了半群O_n(k)的秩为2n-3.进一步,得到了半群O_n(k)(2≤k≤n-1)的幂等元秩为n和半群O_n(1)的幂等元秩为n-1.
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| 关 键 词： | 奇异变换半群 保序 幂等元秩 秩 |
Ranks of the Semigroup O_n(k) |
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| Abstract: | Let O_n be the semigroup of all order-preserving transformations on a finite-chainn].For an arbitrary integer k such that 1≤k≤n-1,the rank and idempotent rank of the semigroup O_n(k)={α∈O_n:(x∈n])x≤kxα≤k} were studied.We show that the rank of semigroup O_n(k) is equal to 2n-3.Furthermore,we obtain that the idempotent rank of the semigroup O_n(k)(1≤k≤n-1) is equal to n,and the rank of the semigroup O_n(1) is equal to n-1. |
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| Keywords: | singular transformation semigroup order-preserving idempotent rank rank |
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