半群T_n(k)的正则性和Green关系
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摘要
设T_n是[n]={1,…,n}上的全变换半群.对任意1≤k≤n,令Tn(k)={α∈T_n|x∈[n],x≤kxα≤k},则Tn(k)是Tn的子半群.刻画了半群GT_n(k)的正则元的特征,并描述了该半群上的Green关系.
Let Tnbe the semigroup of all full transformations of[n]={1,2,…,n}.For 1≤k≤n,let T_n(k)={α∈T_n|x∈[n],x≤k xα≤k}.Then T_n(k)is a subsemigroup of Tn.The characterization of regular elements and Green's relations are given on the semigroup T_n(k).
Let Tnbe the semigroup of all full transformations of[n]={1,2,…,n}.For 1≤k≤n,let T_n(k)={α∈T_n|x∈[n],x≤k xα≤k}.Then T_n(k)is a subsemigroup of Tn.The characterization of regular elements and Green's relations are given on the semigroup T_n(k).
引文
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[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):59-68.
[9]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):59-68.
[9]HOWIE J M.Fundamentals of semigroup theory[M].Oxford:The Clarendon Press,1995:1-349.