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On nilpotent subsemigroups of the order-preserving and decreasing transformation semigroups
Semigroup Forum ( IF 0.7 ) Pub Date : 2020-03-23 , DOI: 10.1007/s00233-020-10098-2
Melek Yağcı , Emrah Korkmaz

Let $${\mathcal {C}}_{n}$$ C n be the semigroup of all order-preserving and decreasing transformations on $$X_{n}=\{1,\ldots ,n\}$$ X n = { 1 , … , n } under its natural order, and let $$N({\mathcal {C}}_{n})$$ N ( C n ) be the subsemigroup of all nilpotent elements of $${\mathcal {C}}_{n}$$ C n . In this paper we determine the minimum generating set of $$N({\mathcal {C}}_n)$$ N ( C n ) , and so the rank of $$N({\mathcal {C}}_n)$$ N ( C n ) . Moreover, we investigate the nilpotent subsemigroups of $${\mathcal {C}}_{n}$$ C n .

中文翻译:

关于保序和降序变换半群的幂零子半群

令 $${\mathcal {C}}_{n}$$ C n 是 $$X_{n}=\{1,\ldots ,n\}$$ X 上所有保序和递减变换的半群n = { 1 , … , n } 在其自然序下,令 $$N({\mathcal {C}}_{n})$$ N ( C n ) 是 $${ 的所有幂零元的子半群\mathcal {C}}_{n}$$ C n 。在本文中,我们确定 $$N({\mathcal {C}}_n)$$ N ( C n ) 的最小生成集,因此 $$N({\mathcal {C}}_n)$ 的秩$ N (CN) 。此外,我们研究了 $${\mathcal {C}}_{n}$$ C n 的幂零子半群。
更新日期:2020-03-23
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