部分注入单元中理想的最大子半群

Pub Date : 2024-05-31 DOI:10.1007/s00233-024-10439-5

Apatsara Sareeto, Jörg Koppitz

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引用次数: 0

摘要

我们研究的是\(POI_n\)这个研究得很好的单元的一个子单元，它是 n 元素链上所有保序局部注入的单元。在 \(POI_n\) 中所有既保留栅栏又保留奇偶性的部分变换的集合 \(IOF_n^{par}\) 构成了 \(POI_n\) 的子单元。我们描述了格林关系和 \(IOF_n^{par}\) 的理想。对于 \(IOF_n^{par}\) 的每个理想，我们描述了最大子半群的特征。我们发现有三种不同类型的最大子群。

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The maximal subsemigroups of the ideals in a monoid of partial injections

We study a submonoid of the well studied monoid \(POI_n\) of all order-preserving partial injections on an n-element chain. The set \(IOF_n^{par}\) of all partial transformations in \(POI_n\) which are fence-preserving as well as parity-preserving forms a submonoid of \(POI_n\). We describe Green’s relations and ideals of \(IOF_n^{par}\). For each ideal of \(IOF_n^{par}\), we characterize the maximal subsemigroups. We observe that there are three different types of maximal subsemigroups.

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