保E~*关系且方向保序部分一一变换半群的Green关系
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摘要
设X为有限集合,E为X上的等价关系且IX是X上的对称逆半群。令IE*(X)={f∈IX:对任意的x,y∈dom(f),(x,y)∈E当且仅当(f(x),f(y))∈E},则IE*(X)是IX的逆子半群。设X为全序集,E为X上的凸等价关系。令OPIE*(X)为IE*(X)中所有方向保序部分一一变换作成的半群。这是一类全新的半群,有一定的难度和复杂性,通过对它的研究可以探求新的变换半群的结构与性质。本文讨论它的Green关系。
Let IXbe the symmetric inverse semigroup on the finite set Xand Ean equivalence on X.Let IE*(X)={f∈IX :for arbitrary elements x,y ∈dom(f),(x,y)∈Eif and only if(f(x),f(y))∈E}.Then IE*(X)forms an inverse subsemigroup of IX.If X is a totally ordered set and E is convex equivalence on X,then let OPIE*(X)be a semigroup consisting of all preserving orientation partial oneone transformations in IE*(X).It is a new class of semigroup and its research is difficult and complicated.By studying it,some new structure and properties of semigroups are explored.Green's relations on OPIE*(X)are described in this paper.
Let IXbe the symmetric inverse semigroup on the finite set Xand Ean equivalence on X.Let IE*(X)={f∈IX :for arbitrary elements x,y ∈dom(f),(x,y)∈Eif and only if(f(x),f(y))∈E}.Then IE*(X)forms an inverse subsemigroup of IX.If X is a totally ordered set and E is convex equivalence on X,then let OPIE*(X)be a semigroup consisting of all preserving orientation partial oneone transformations in IE*(X).It is a new class of semigroup and its research is difficult and complicated.By studying it,some new structure and properties of semigroups are explored.Green's relations on OPIE*(X)are described in this paper.
引文
[1]HOWIE J M.Fundamentals of semigroup of theory[M].Oxford:Oxford University Press,1995.
[2]FERNANDES V H.The monoid of all injective orientation preserving partial transformations on a finite chain[J].Communications in Algebra,2000,28(7):3401-3426.
[3]FERNANDES V H.The monoid of all injective order preserving partial transformation on a finite chain[J].Semigroup Forum,2001,62(2):178-204.
[4]PEI Hui-sheng.Regularity and green’s relations for semigroups of transformations that preserve an equivalence[J].Communications in Algebra,2005,33(1):109-118.
[5]DENG Lun-zhi,ZENG Ji-wen,YOU Tai-jie.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.
[6]龙伟锋,游泰杰,龙伟芳,等.保E*关系的部分一一变换半群[J].西南大学学报:自然科学版,2013,35(4):63-66.
[7]龙伟锋,游泰杰.IE*(X)中E类方向保序变换半群的秩[J].数学的实践与认识,2014,44(10):230-234.
[8]龙伟锋,徐波,游泰杰,等.保E且严格保序部分一一变换半群的秩[J].四川师范大学学报:自然科学版,2014,37(3):316-319.
[9]ZHAO Ping,YANG Mei.Regularity and Green’s relations on semigroups of transformation preserving order and compression[J].Bulletin of the Korean Mathematical Society,2012,49(5):1015-1025.
[10]HOWIE J M.An introduction to semigroup theory[M].London:Academic Press,1976.
[2]FERNANDES V H.The monoid of all injective orientation preserving partial transformations on a finite chain[J].Communications in Algebra,2000,28(7):3401-3426.
[3]FERNANDES V H.The monoid of all injective order preserving partial transformation on a finite chain[J].Semigroup Forum,2001,62(2):178-204.
[4]PEI Hui-sheng.Regularity and green’s relations for semigroups of transformations that preserve an equivalence[J].Communications in Algebra,2005,33(1):109-118.
[5]DENG Lun-zhi,ZENG Ji-wen,YOU Tai-jie.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.
[6]龙伟锋,游泰杰,龙伟芳,等.保E*关系的部分一一变换半群[J].西南大学学报:自然科学版,2013,35(4):63-66.
[7]龙伟锋,游泰杰.IE*(X)中E类方向保序变换半群的秩[J].数学的实践与认识,2014,44(10):230-234.
[8]龙伟锋,徐波,游泰杰,等.保E且严格保序部分一一变换半群的秩[J].四川师范大学学报:自然科学版,2014,37(3):316-319.
[9]ZHAO Ping,YANG Mei.Regularity and Green’s relations on semigroups of transformation preserving order and compression[J].Bulletin of the Korean Mathematical Society,2012,49(5):1015-1025.
[10]HOWIE J M.An introduction to semigroup theory[M].London:Academic Press,1976.