关于反射等价关系的变换半群的注记A note on naturally ordered semigroups of transformations of a set that reflect an equivalence relation
孙俊岭,孙垒
摘要(Abstract)：
设TX是非空集合X上全变换半群,E是X上非平凡的等价关系,则T?(X)是TX的子半群.在赋予半群T?(X)自然偏序关系的条件下,本文刻画了它的相容元.
关键词(KeyWords)： 变换半群;自然偏序关系;相容元
基金项目(Foundation): 国家自然科学基金(U1404101);; 河南省教育厅科学技术研究重点项目基础研究计划(14A110003)
作者(Author): 孙俊岭,孙垒
参考文献(References)：
- [1]Mitsch H.A natural partial order for semigroups[J].Proceedings of the American Mathematical Society,1986,97(3):384-388.
- [2]Kowol G,Mitsch H.Naturally ordered transformation semigroups[J].Monatshefte Fur Mathematik,1986,102(2):115-138.
- [3]Marques-Smith M Paula O,Sullivan R P.Partial orders on transformation semigroups[J].Monatshefte Fur Mathematik,2003,140(2):103-118.
- [4]Sullivan R P.Partial orders on linear transformation semigroups[J].Proceedings of the Royal Society Edinburgh Section A-Mathematics,2005,135(2):413-437.
- [5]Sun L,Deng W N,Pei H S.Naturally ordered transformation semigroups preserving an equivalence and a cross-section[J].Algebra Colloquium,2011,18(3):523-532.
- [6]Deng L Z,Zeng J W,You T J.Green′s relations and regularity for semigroups of transformations that preserve reverse direction equivalence[J].Semigroup Forum,2011,83(3):489-498.
- [7]Sun L,Xin X J.The natural partial order on the semigroup of all transformations of a set that reflect on equivalence relation[J].Bullet of the Australian Mathematical Society,2013,88(3):359-368.