保等价关系变换半群的变种半群上的自然偏序
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摘要
在保等价变换半群上规定新的运算,通过此运算,得到保等价变换半群的变种半群.给出了此半群中自然偏序关系的定义,利用定义,考察了半群中两个元素何时关于此偏序关系是相关的,并探讨了关于这个关系相容的元素,所得结果推广了保等价变换半群上的自然偏序关系.
A new calculation on transformation semigroup preserving equivalence relation is defined and its variant semigroup derived.The definition of the natural order of the variant semigroup is given,and based on the definition,conditions that the two elements of the variant semigroup are related under the natural order are examined.Meanwhile,the elements about the natural order which are compatible are discussed.Then,the study of the natural order of transformation semigroup preserving equivalence relation is promoted.
A new calculation on transformation semigroup preserving equivalence relation is defined and its variant semigroup derived.The definition of the natural order of the variant semigroup is given,and based on the definition,conditions that the two elements of the variant semigroup are related under the natural order are examined.Meanwhile,the elements about the natural order which are compatible are discussed.Then,the study of the natural order of transformation semigroup preserving equivalence relation is promoted.
引文
[1]VAGNER V V.Generalized groups[J].Doklady Akademii Nauk SSSR,1952,84:H19-1122.
[2]NAMBOORIPAD K S.The natural partial order on a regular semigroup[J].Proceedings of the Edinburgh Mathematical Society,1980,23:249-260.
[3]MITSCH H.A natural partial order for semigroups[J].Proceedings of the American Mathematical Society,1986,97:384-388.
[4]PEI H S.Regularity and Green's relations for semigroups of transformations that preserve an equivalence[J].Communications in Algebra,2005,33(1):109-118.
[5]SUN L,PEI H S,CHENG Z X.Naturally ordered transformation semigroups preserving an equivalence[J].Bulletin of the Australian Mathematical Society,2008,78(2):117-128.
[6]裴惠生,邓伟娜.保持序和等价关系的自然偏序变换半群[J].数学学报,2012,55(2):235-250.
[7]PEI H S,SUN L,ZHAI H C.Green's relations for the variants of transformation semigroups preserving an equivalence relation[J].Communications in Algebra,2007,35(6):1971-1986.
[2]NAMBOORIPAD K S.The natural partial order on a regular semigroup[J].Proceedings of the Edinburgh Mathematical Society,1980,23:249-260.
[3]MITSCH H.A natural partial order for semigroups[J].Proceedings of the American Mathematical Society,1986,97:384-388.
[4]PEI H S.Regularity and Green's relations for semigroups of transformations that preserve an equivalence[J].Communications in Algebra,2005,33(1):109-118.
[5]SUN L,PEI H S,CHENG Z X.Naturally ordered transformation semigroups preserving an equivalence[J].Bulletin of the Australian Mathematical Society,2008,78(2):117-128.
[6]裴惠生,邓伟娜.保持序和等价关系的自然偏序变换半群[J].数学学报,2012,55(2):235-250.
[7]PEI H S,SUN L,ZHAI H C.Green's relations for the variants of transformation semigroups preserving an equivalence relation[J].Communications in Algebra,2007,35(6):1971-1986.