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薛琳, 孙垒. 一类变换半群的左相容元[J]. 信阳师范学院学报(自然科学版), 2015, 28(4): 472-474. DOI: 10.3969/j.issn.1003-0972.2015.04.002
引用本文: 薛琳, 孙垒. 一类变换半群的左相容元[J]. 信阳师范学院学报(自然科学版), 2015, 28(4): 472-474. DOI: 10.3969/j.issn.1003-0972.2015.04.002
shu
Xue Lin , Sun Lei . Left Compatible Elements in Certain Transformation Semigroups[J]. Journal of Xinyang Normal University (Natural Science Edition), 2015, 28(4): 472-474. DOI: 10.3969/j.issn.1003-0972.2015.04.002
Citation: Xue Lin , Sun Lei . Left Compatible Elements in Certain Transformation Semigroups[J]. Journal of Xinyang Normal University (Natural Science Edition), 2015, 28(4): 472-474. DOI: 10.3969/j.issn.1003-0972.2015.04.002
shu

一类变换半群的左相容元

Left Compatible Elements in Certain Transformation Semigroups

    摘要
  • 摘要: 设 T X 是非空集合 X 上全变换半群, E 是 X 上非平凡的等价关系, R 是 X / E 的横断面, 则T E ( X , R ) = f ∈ T X : ∀ x , y ∈ X , ( x , y ) ∈ E ⇒ ( f ( x ) , f ( y ) ) ∈ E 且 f ( R ) ⊆ R 是 T X 的子半群 . 本文赋予半群 T E ( X , R ) 自然偏序关系, 通过构造映射的方法, 刻画它的左相容元, 给出充要条件 .

     

    Abstract: Let TX be the full transformation semigroup on a nonempty set X, E be a nontrivial equivalence relation on Xand R be a cross-section of X/E, then TE(X,R)=f∈TX:∀x,y∈X,(x,y)∈E ⇒(f(x),f(y))∈E and f(R)⊆Ris a subsemigroup of T、X. By constructing suitable mappings, all the left compatible elements were described in the transformation semigroup TE(X,R) endowed with the natural partial order and a necessary and sufficient condition for these elements was given

     

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