一类半群的正则性和格林关系
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摘要
设E是X上的一个等价关系,P_E(X)是由等价关系E确定的保等价关系的部分变换半群.利用格林关系和正则元的定义,研究了半群P_E(X)的一个子半群P_2(X)={f∈P_E(X)∶|imf|≤2}上的格林关系和正则性,刻画了半群P2(X)上的两元素间的格林关系,给出了这类半群中元素为正则元的充要条件.
Let Ebe an equivalence on Xand P_E(X)is a partial transformation semigroup of preserving equivalence relations determined by the equivalence E.Using the definition of Green's-relations and regular elements,the Green's-relations and regularity on semigroup P_2(X)={f∈PE(X)∶|imf|≤2}the subsemigroup of PE(X)are studied and the Green's-relations of semigroup P_2(X)is described,and the sufficient and necessary condition of semigroup whose elements are regular are given.
Let Ebe an equivalence on Xand P_E(X)is a partial transformation semigroup of preserving equivalence relations determined by the equivalence E.Using the definition of Green's-relations and regular elements,the Green's-relations and regularity on semigroup P_2(X)={f∈PE(X)∶|imf|≤2}the subsemigroup of PE(X)are studied and the Green's-relations of semigroup P_2(X)is described,and the sufficient and necessary condition of semigroup whose elements are regular are given.
引文
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[2]邓伟娜,裴惠生.一类保持等价关系的变换半群的正则性和格林关系[J].信阳师范学院学报(自然科学版),2012,25(3):281-284.Deng Weina,Pei Huisheng.Regularity and Green’s relations for a semigroup of transformations preserving an equivalence relation[J].Journal of Xinyang Normal University(Natural Science Edition),2012,25(3):281-284.(in Chinese)
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[5]秦美青,许新斋.保等价部分变换半群的变种半群上的正则元[J].纯粹数学与应用数学,2010,26(5):822-827.Qin Meiqing,Xu Xinzhai.The regular element for bariant semigroup of partial transformation semigroup preserving an equivalence relation[J].Pure and Applied Mathematics,2010,26(5):822-827.(in Chinese)
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[8]孙垒,裴惠生.一类广义变换半群的格林关系[J].纯粹数学与应用数学,2010,26(1):73-78.Sun Lei,Pei Huisheng.Green’s relations on a kind of generalized transformation semigrop[J].Pure and Applied Mathematics,2010,26(1):73-78.(in Chinese)
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[10]陈辉蓉.半群PTn(A)的正则性与格林关系[J].数学的实践与认识,2012,42(23):202-206.Chen Huirong.Regularity and Green’s relations on a semigroups of PTn(A)[J].Mathematics in Practice and Theory,2012,42(23):202-206.(in Chinese)
[11]宋家彬,滕文,丁訸.一类变种半群的格林关系和正则性[J].贵州师范学院学报,2012,28(9):4-7.Song Jiabin,Teng Wen,Ding He.Green’s relations and regularity of a kind of variants semi-group[J].Journal of Guizhou Normal College,2012,28(9):4-7.(in Chinese)
[12]赵颐,游泰杰.半群CPOn(A)的格林关系[J].扬州大学学报(自然科学版),2015,18(4):5-8.Zhao Yi,You Taijie.Green’s relations on the semigroup CPOn(A)[J].Journal of Yangzhou University(Natural Science Edition),2015,18(4):5-8.(in Chinese)
[13]龙伟峰,徐波.保E*关系且方向保序部分一一变换半群的Green关系[J].广西师范大学学报(自然科学版),2014,32(4):72-75.Long Weifeng,Xu Bo.The Green’s relation for semigroup of preserving an E*relation and orientation partial one-one transformation[J].Journal of Guangxi Normal University(Natural Science Edition),2014,32(4):72-75.(in Chinese)
[14]秦美青.一类变种半群上的格林*关系[J].纯粹数学与应用数学,2015,31(5):480-486.Qin Meiqing.The Green’s*-relations on a class of transformation semigrop[J].Pure and Applied Mathematics,2015,31(5):480-486.(in Chinese)
[15]钟艳林,邓伦治.欧氏空间中升序变换半群的格林关系和正则元[J].数学的实践与认识,2013,43(24):198-201.Zhong Yanlin,Deng Lunzhi.Green’s relations and regularity for semigroups of order-increasing transformations on euclidean space[J].Mathematics in Practice and Theory,2013,43(24):198-201.(in Chinese)
[16]罗永贵,瞿云云.半群PO(X,Y,θ)的格林关系及正则元[J].云南民族大学学报(自然科学版),2014,23(6):434-438.Luo Yonggui,Qu Yunyun.Green’s relations and regularity for the semigroup PO(X,Y,θ)[J].Journal of Yunnan Minzu University(Natural Science Edition),2014,23(6):434-438.(in Chinese)
[2]邓伟娜,裴惠生.一类保持等价关系的变换半群的正则性和格林关系[J].信阳师范学院学报(自然科学版),2012,25(3):281-284.Deng Weina,Pei Huisheng.Regularity and Green’s relations for a semigroup of transformations preserving an equivalence relation[J].Journal of Xinyang Normal University(Natural Science Edition),2012,25(3):281-284.(in Chinese)
[3]Pei Huisheng,Zhou Huijuan.Semigroups of partial transformatons preserving an equivalence relation[J].数学进展,2009,38(1):103-118.
[4]Pei Huisheng,Sun Lei,Zhai Honcun.Green’s relations for the variants of transformation semigroups preserving an equivalence relation[J].Communications in Algebra,2007,35:1971-1986.
[5]秦美青,许新斋.保等价部分变换半群的变种半群上的正则元[J].纯粹数学与应用数学,2010,26(5):822-827.Qin Meiqing,Xu Xinzhai.The regular element for bariant semigroup of partial transformation semigroup preserving an equivalence relation[J].Pure and Applied Mathematics,2010,26(5):822-827.(in Chinese)
[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.Pei Huisheng,Deng Weina.Naturally ordered transformation semigroup preserving order and an equivalence relation[J].Acta Mathematica Sinica,2012,55(2):235-250.(in Chinese)
[7]Pei Huisheng,Zou Dingyu.Green’s Equivalences on semigroups of transformation preserving order and an equivalence relation[J].Semigroup Forum,2005,71(2):241-251.
[8]孙垒,裴惠生.一类广义变换半群的格林关系[J].纯粹数学与应用数学,2010,26(1):73-78.Sun Lei,Pei Huisheng.Green’s relations on a kind of generalized transformation semigrop[J].Pure and Applied Mathematics,2010,26(1):73-78.(in Chinese)
[9]Howie J M.Fundamentals of Semigroup Theory[M].New York:Oxford University Press,1995.
[10]陈辉蓉.半群PTn(A)的正则性与格林关系[J].数学的实践与认识,2012,42(23):202-206.Chen Huirong.Regularity and Green’s relations on a semigroups of PTn(A)[J].Mathematics in Practice and Theory,2012,42(23):202-206.(in Chinese)
[11]宋家彬,滕文,丁訸.一类变种半群的格林关系和正则性[J].贵州师范学院学报,2012,28(9):4-7.Song Jiabin,Teng Wen,Ding He.Green’s relations and regularity of a kind of variants semi-group[J].Journal of Guizhou Normal College,2012,28(9):4-7.(in Chinese)
[12]赵颐,游泰杰.半群CPOn(A)的格林关系[J].扬州大学学报(自然科学版),2015,18(4):5-8.Zhao Yi,You Taijie.Green’s relations on the semigroup CPOn(A)[J].Journal of Yangzhou University(Natural Science Edition),2015,18(4):5-8.(in Chinese)
[13]龙伟峰,徐波.保E*关系且方向保序部分一一变换半群的Green关系[J].广西师范大学学报(自然科学版),2014,32(4):72-75.Long Weifeng,Xu Bo.The Green’s relation for semigroup of preserving an E*relation and orientation partial one-one transformation[J].Journal of Guangxi Normal University(Natural Science Edition),2014,32(4):72-75.(in Chinese)
[14]秦美青.一类变种半群上的格林*关系[J].纯粹数学与应用数学,2015,31(5):480-486.Qin Meiqing.The Green’s*-relations on a class of transformation semigrop[J].Pure and Applied Mathematics,2015,31(5):480-486.(in Chinese)
[15]钟艳林,邓伦治.欧氏空间中升序变换半群的格林关系和正则元[J].数学的实践与认识,2013,43(24):198-201.Zhong Yanlin,Deng Lunzhi.Green’s relations and regularity for semigroups of order-increasing transformations on euclidean space[J].Mathematics in Practice and Theory,2013,43(24):198-201.(in Chinese)
[16]罗永贵,瞿云云.半群PO(X,Y,θ)的格林关系及正则元[J].云南民族大学学报(自然科学版),2014,23(6):434-438.Luo Yonggui,Qu Yunyun.Green’s relations and regularity for the semigroup PO(X,Y,θ)[J].Journal of Yunnan Minzu University(Natural Science Edition),2014,23(6):434-438.(in Chinese)