保持双向等价关系的变换半群自然偏序关系的若干结果
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摘要
设X为任意的非空集合,T X是X上的全变换半群.设E是X上的一个等价关系,T E*(X)是由等价关系E所决定的T X的子半群,满足(x,y)∈E当且仅当(f(x),(fy))∈E.将讨论T E*(X)中的变换在自然偏序关系下的覆盖元以及任意两个变换的上(下)界.
Let X be an arbitrary nonempty set,T X is the full transformation semigroup on X. Let E be an equivalence relation on X,T E*(X)is a subsemigroup of T X determined by E which satisfies(x,y)∈E if and only if(f(x),(fy))∈E. In this paper,the covering elements of T E*(X)under the natural order are described,and the lowe(rupper)bound of two elements is discussed.
Let X be an arbitrary nonempty set,T X is the full transformation semigroup on X. Let E be an equivalence relation on X,T E*(X)is a subsemigroup of T X determined by E which satisfies(x,y)∈E if and only if(f(x),(fy))∈E. In this paper,the covering elements of T E*(X)under the natural order are described,and the lowe(rupper)bound of two elements is discussed.
引文
[1]Kowol G,Mirsch H.Naturally ordered transformation semigroup[J].Monatsh Math,1986,102:115-138.
[2]Sun Lei,Pei Huisheng,Cheng Zhenxing.Naturally ordered transformation semigroups preserving an equivalence[J].Bull Austral Math Soc,2008,78:117-128.
[3]Pei Huisheng,Deng Weina.The Natural order for the E-order-preserving transformation semigroup[J].Asian-European Journal of Mathematics,2012,5(3):1250035(1-14).
[4]Deng Lunzhi,Zeng Jiwen,Xu Bo.Green’s Relations and Regularity for semigroups of Transformations that preserve Double Direction Equivalence[J].Semigroup Forum,2010,80:416-425.
[5]裴惠生,邓伟娜.保持双向等价关系的变换半群的若干结果[J].西南大学学报,2012,34(8):2-5.
[6]Sun Lei,Sun Junling.A partial order on transformation semigroups that preserve double direction equivalence relation[J].Journal of Algebra and Its Applications,accepted 22 January 2013,to appear.
[7]邓伟娜,裴惠生.一类保持等价关系变换半群的正则性和格林关系[J].信阳师范学院学报,2012,25(3):281-284.
[2]Sun Lei,Pei Huisheng,Cheng Zhenxing.Naturally ordered transformation semigroups preserving an equivalence[J].Bull Austral Math Soc,2008,78:117-128.
[3]Pei Huisheng,Deng Weina.The Natural order for the E-order-preserving transformation semigroup[J].Asian-European Journal of Mathematics,2012,5(3):1250035(1-14).
[4]Deng Lunzhi,Zeng Jiwen,Xu Bo.Green’s Relations and Regularity for semigroups of Transformations that preserve Double Direction Equivalence[J].Semigroup Forum,2010,80:416-425.
[5]裴惠生,邓伟娜.保持双向等价关系的变换半群的若干结果[J].西南大学学报,2012,34(8):2-5.
[6]Sun Lei,Sun Junling.A partial order on transformation semigroups that preserve double direction equivalence relation[J].Journal of Algebra and Its Applications,accepted 22 January 2013,to appear.
[7]邓伟娜,裴惠生.一类保持等价关系变换半群的正则性和格林关系[J].信阳师范学院学报,2012,25(3):281-284.