半群LD(n,r)的极大正则子半群
Maximal Regular Subsemigroups of the Semigroup LD(n, r)
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摘要: 设自然数n≥4,Don是有限链[n]上的保反序奇异变换半群.对任意的r(1≤r≤n-1),记LD(n,r)={α∈Don:|im(α)|≤r}为半群Don的双边理想.通过对秩为r的幂等元和格林关系的分析,获得了半群LD(n,r)的极大正则子半群的完全分类.Abstract: Let DOn be the semigroup of all order-reversing singular transformations on a finite-chain [n] if n≥4, and let LD(n, r)={α∈DOn: |im(α)|≤r} be the two-sided ideal of the semigroup DOn if for an arbitrary integer r such that 1≤r≤n-1.By analyzing the idempotent of rank r and Green`s relations, the classification of the maximal regular subsemigroup of the semigroup LD(n, r) is completely obtained.
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