裴惠生. 一类有限变换半群的Green关系[J]. 信阳师范学院学报(自然科学版), 2002, 15(3): 258-261.
引用本文: 裴惠生. 一类有限变换半群的Green关系[J]. 信阳师范学院学报(自然科学版), 2002, 15(3): 258-261.
PEI Hui sheng. Green’s relations for a kind of finite transformation semigroups[J]. Journal of Xinyang Normal University (Natural Science Edition), 2002, 15(3): 258-261.
Citation: PEI Hui sheng. Green’s relations for a kind of finite transformation semigroups[J]. Journal of Xinyang Normal University (Natural Science Edition), 2002, 15(3): 258-261.

一类有限变换半群的Green关系

Green’s relations for a kind of finite transformation semigroups

  • 摘要: 在 5中作者考察过一类变换半群 ,即 TE(X) = f∈TX: (a,b)∈ E,(f(a) ,f(b) )∈ E,这里 E是集合 X上任一等价关系 .当 X带上以所有 E类为基的拓扑时 ,TE(X)恰是拓扑空间 X上的连续自映射半群 .本文讨论了半群 TE(X)上的 Green关系 ,并且当 X为有限集 ,E是单等价关系时 ,给出了全部 Green关系的刻划 .

     

    Abstract: In ,the author observed a class of transformation semigroups,namely T E(X)=f∈T X:(a,b)∈E,(f(a),f(b))∈E,where E is an equivalence on the set X.If X carries the topology generated by the basis consisting of all E classes.then T E(X) is exactly the semigroup of all continuous selfmaps of the space X.In this paper,Green's relations on T E(X) are consided and completely characterized in the case that X is finite and E is simple.

     

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