半群P_n(k)的正则性和Green关系
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摘要
设P_n是X_n={1,…,n}上的部分变换半群.对任意1≤k≤n,令P_n(k)={α∈P_n:(x∈dom(α)x≤k■xα≤k},则易验证P_n(k)是P_n的子半群.刻画了半群P_n(k)的正则元的特征,并且描述了这个半群上的Green关系.
Let P_n be the semigroup of all partial transformations of X_n={1,2,…,n}.For 1
Let P_n be the semigroup of all partial transformations of X_n={1,2,…,n}.For 1
引文
[1]Green J A.On the structure of semigroups[J].Ann Math,1951,54(2):163-172.
[2]Pei H S.Regularity and Green's relations for semigroups of transformations which preserve an equivalences[J].Communications in Algebra,2005,33(1):109-118.
[3]Pei H S,Zou D Y.Green's equivalences on semigroups of transformations preserving order and an equivalence[J].Semigroup Forum,2005,71(2):241-251.
[4]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.
[5]Sun L,Pei H S.Regularity and Green's relations for semigroups of transformations preserving orientation and an equivalence[J].Semigroup Forum,2007,74(3):473-486.
[6]Deng L Z,Zeng J W,Xu B.Green's relations and regularity for semigroups of transformations that preserve double direction equivalence[J].Semigroup Forum,2010,80(3):416-425.
[7]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.
[8]Deng L Z,Zeng J W,You T J.Green's relations and regularity for semigroups of transformations that preserve order and a double direction equivalence[J].Semigroup Forum,2012,84(1):59-60.
[9]Zhao P,Yang M.Regularity and Green's relations on semigroups of transformation preserving order and compression[J].Bull Korean Math Soc,2012,49(5):1015-1025.
[10]Howie J M.Fundamentals of semigroup theory[M].Oxford:The Clarendon Press,1995,1-349.
[2]Pei H S.Regularity and Green's relations for semigroups of transformations which preserve an equivalences[J].Communications in Algebra,2005,33(1):109-118.
[3]Pei H S,Zou D Y.Green's equivalences on semigroups of transformations preserving order and an equivalence[J].Semigroup Forum,2005,71(2):241-251.
[4]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.
[5]Sun L,Pei H S.Regularity and Green's relations for semigroups of transformations preserving orientation and an equivalence[J].Semigroup Forum,2007,74(3):473-486.
[6]Deng L Z,Zeng J W,Xu B.Green's relations and regularity for semigroups of transformations that preserve double direction equivalence[J].Semigroup Forum,2010,80(3):416-425.
[7]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.
[8]Deng L Z,Zeng J W,You T J.Green's relations and regularity for semigroups of transformations that preserve order and a double direction equivalence[J].Semigroup Forum,2012,84(1):59-60.
[9]Zhao P,Yang M.Regularity and Green's relations on semigroups of transformation preserving order and compression[J].Bull Korean Math Soc,2012,49(5):1015-1025.
[10]Howie J M.Fundamentals of semigroup theory[M].Oxford:The Clarendon Press,1995,1-349.