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The monoid of all orientation-preserving and extensive full transformations on a finite chain
Journal of Algebra and Its Applications ( IF 0.5 ) Pub Date : 2021-02-22 , DOI: 10.1142/s0219498822501055 De Biao Li 1, 2 , Wen Ting Zhang 1, 2 , Yan Feng Luo 1, 2
Journal of Algebra and Its Applications ( IF 0.5 ) Pub Date : 2021-02-22 , DOI: 10.1142/s0219498822501055 De Biao Li 1, 2 , Wen Ting Zhang 1, 2 , Yan Feng Luo 1, 2
Affiliation
Let 𝒪 𝒫 ℰ n be the monoid of all orientation-preserving and extensive full transformations on { 1 , 2 , … , n } ordered in the standard way. In this paper, we determine the minimum generating set and the minimum idempotent generating set of 𝒪 𝒫 ℰ n , and so the rank and the idempotent rank of 𝒪 𝒫 ℰ n are obtained. Moreover, we describe maximal subsemigroups and maximal idempotent generated subsemigroups of 𝒪 𝒫 ℰ n and completely obtain their classifications.
中文翻译:
有限链上所有保向和扩展全变换的幺半群
让𝒪 𝒫 ℰ n 是所有方向保持和广泛的全变换的幺半群{ 1 , 2 , … , n } 以标准方式订购。在本文中,我们确定了最小生成集和最小幂等生成集𝒪 𝒫 ℰ n ,所以秩和幂等秩𝒪 𝒫 ℰ n 获得。此外,我们描述了最大子半群和最大幂等生成子半群𝒪 𝒫 ℰ n 并完全获得它们的分类。
更新日期:2021-02-22
中文翻译:
有限链上所有保向和扩展全变换的幺半群
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