Let 𝒪𝒫ℰn 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 𝒪𝒫ℰn, and so the rank and the idempotent rank of 𝒪𝒫ℰn are obtained. Moreover, we describe maximal subsemigroups and maximal idempotent generated subsemigroups of 𝒪𝒫ℰn and completely obtain their classifications.

中文翻译：

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有限链上所有保向和扩展全变换的幺半群

让𝒪𝒫ℰn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𝒪𝒫ℰn，所以秩和幂等秩𝒪𝒫ℰn获得。此外，我们描述了最大子半群和最大幂等生成子半群𝒪𝒫ℰn并完全获得它们的分类。