孙垒, 李佳阳. 降序变换半群${ \Large S_n^-}$上的自然偏序关系[J]. 云南大学学报(自然科学版), 2020, 42(1): 14-18. doi: 10.7540/j.ynu.20180143
引用本文: 孙垒, 李佳阳. 降序变换半群${ \Large S_n^-}$上的自然偏序关系[J]. 云南大学学报(自然科学版), 2020, 42(1): 14-18. doi: 10.7540/j.ynu.20180143
SUN Lei, LI Jia-yang. A natural partial order on the semigroups ${ \Large S_n^-}$ of order-decreasing transformations[J]. Journal of Yunnan University: Natural Sciences Edition, 2020, 42(1): 14-18. DOI: 10.7540/j.ynu.20180143
Citation: SUN Lei, LI Jia-yang. A natural partial order on the semigroups ${ \Large S_n^-}$ of order-decreasing transformations[J]. Journal of Yunnan University: Natural Sciences Edition, 2020, 42(1): 14-18. DOI: 10.7540/j.ynu.20180143

降序变换半群 \Large S_n^-上的自然偏序关系

A natural partial order on the semigroups \Large S_n^- of order-decreasing transformations

  • 摘要:T_X 是全序集 X = \left\ 1 <2 < \cdots < n \right\ 上的全变换半群,则 S_n^ - = \ f \in T_X:\forall x \in X,f(x) \leqslant x\ T_X 的降序变换子半群. 赋予降序变换半群 S_n^ - 自然偏序关系,给出了 S_n^ - 的特征,刻画了 S_n^ - 的相容元,描述了 S_n^ - 的极小元和极大元.

     

    Abstract: Let T_X be the full transformation semigroup on a total order set X = \ 1 <2 < \cdots < n\ . Then S_n^ - = \left\ f \in T_X:\forall x \in X,f(x) \le x \right\ is a subsemigroup of T_X. We endow the order-decreasing transformation semigroup S_n^ - with the natural partial order. With respect to this partial order, we investigate when two elements of \Large S_n^- are related, then find elements of \Large S_n^- which are compatible with the order. Also, we characterize the minimal elements and the maximal elements of \Large S_n^- .

     

/

返回文章
返回