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保持双向等价关系的变换半群的一些结果

Some Results of Transformation Semigroups that Preserve Double Direction Equivalences
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摘要 设X为非空集合,E是X上的等价关系,T(X)是X上的全变换半群.记T_(E*)(X)={α∈T(X)|(∀x,y∈X)(x,y)∈E⇔(xα,yα)∈E},则T_(E*)(X)是T(X)的子半群.许多学者对半群T_(E*)(X)作了研究,而沿着这些方向继续研究还可以刻画出T_(E*)(X)中的关系L˜,给出L*=L˜,R=R*的充要条件,证明T_(E*)(X)中的正则元集Re g(T_(E*)(X))形成子半群,同时可以得到Re g(T_(E*)(X))构成完全正则半群和纯正半群的充要条件. Let X be a non-empty set,E an equivalence relation on X and T(X)the full transformation semigroup on X.Let T_(E*)(X)={α∈T(X)|(∀x,y∈X)(x,y)∈E⇔(xα,yα)∈E},then T_(E*)(X)is a subsemigroup of T(X),which has been studied by many scholars.Continuous study along these directions can describe the L˜-relation of T_(E*)(X),give the necessary and sufficient conditions for L*=L˜and R*=R,and prove that the set of regular elements Reg(T_(E*)(X))of T_(E*)(X)forms a regular subsemigroup.The necessary and sufficient conditions can also be obtained for that Reg(T_(E*)(X))is a completely regular semigroup or an orthodox semigroup.
作者 陈辉 刘鑫 王守峰 CHEN Hui;LIU Xin;WANG Shoufeng(School of Mathematics,Yunnan Normal University,Kunming 650500,China)
出处 《玉溪师范学院学报》 2022年第3期11-15,共5页 Journal of Yuxi Normal University
基金 国家自然科学基金资助项目(项目编号:11661082).
关键词 等价关系 格林*-关系 格林~-关系 纯正半群 完全正则半群 equivalence relation Green’s*-relation Green~-relation orthodox semigroup completely regular semigroup
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  • 1K.P.Shum.The structure of superabundant semigroups[J].Science China Mathematics,2004,47(5):756-771. 被引量:12
  • 2SHUM K.P..A generalized Clifford theorem of semigroups[J].Science China Mathematics,2010,53(4):1097-1101. 被引量:6
  • 3HOWIE J M. Fundamentals of Semigroup Theory[M]. Oxford: Oxford University Press, 1995.
  • 4FOUNTAIN J B. Abundant Semigroups [J]. Proc London Math Soc, 1982, 44: 103-129.
  • 5UMAR A. On the Semigroups of Order-Decreasing Finite Full Transformations[J]. Proc Roy Soc Edinburgh: Sect A, 1992, 120: 129-142.
  • 6PEI Hui-sheng. Equivalences, a-Semigroups and a-Congruences [J]. Semigroup Forum, 1994, 49: 49- 58.
  • 7PEI Hui-sheng. Regularity and Green's Relations for Semigroups of Transformations that Preserve an Equivalence [J]. Communications in Algebra, 2005, 33: 109-118.
  • 8PEI Hui-sheng, ZHOU Hui-juan. Abundant Semigroups of Transformations Preserving an Equivalence Relation[J]. Algebra Colloquium, 2011, 18(1):77- 82.
  • 9PEI Hui-sheng, DENG Wei-na. A Note on Green's Relations in the Semigroups T(X, p) [J].Semigroup Forum, 2009, 79: 210-213.
  • 10DENG Lun-zhi, ZENG Ji-wen, XU Bo. Green's Relations and Regularity for Semigroups of Transformations that Pre- serve Double Direction Equivalence [J]. Semigroup Forum, 2010, 80: 416-425.

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