正则ω~2-半群
|
摘要
正则ω~2-半群可分为有核和无核2种情况.获得了无核的正则ω~2-半群的一个刻画,并给出具有真核的正则ω~2-半群的结构定理以及相应于这一结构的同构定理.
Regular ω~2-semigroups can be divided into two kinds,one with kernel and the other without kernels.A characterization for regular semigroups without kernels is obtained in this paper.Then the structure theorem for regular ω~2-semigroups with a proper kernel,and the isomorphism theorem corresponding to this structure are also presented.
Regular ω~2-semigroups can be divided into two kinds,one with kernel and the other without kernels.A characterization for regular semigroups without kernels is obtained in this paper.Then the structure theorem for regular ω~2-semigroups with a proper kernel,and the isomorphism theorem corresponding to this structure are also presented.
引文
[1]HOWIE J M.Fundamentals of semigroup theory[M].Oxford:Clarendon Press,1995.
[2]PETRICH M.Inverse semigroups[M].New York:Wiley-Interscience,1984.
[3]SHANG Y,WANG L M.A class of regular simpleω2-semigroups-I[J].Advances in Mathematics(China),2013,42:631-643.
[4]SHANG Y,WANG L M,FENG Y Y.A class of regular simpleω2-semigroups-II[J].Communications in Mathematical Research,2013,29(4):351-362.
[5]CHEN H,HUANG H,GUO X J.On q*-bisimple IC semigroups of type E[J].Semigroup Forum,2009,78(1):106-117.
[6]GUO X J,SHUM.K.P.On translational hulls of type-A semigroups[J].J Algebra,2003,269(1):240-249.
[7]SHUM K P,DU L,GUO Y Q.Green's relations and their generalizations on semigroups[J].Discuss Math Gen Algebra Appl,2010,30(1):71-89.
[8]秦美青.保等价关系变换半群的变种半群上的自然偏序[J].华东师范大学学报:自然科学版,2017(2):29-34.QIN M Q.Natural order on variant semigroup of transformation semigroup preserving equivalence relation[J].Journal of East China Normal University:Natural Sciences Edition,2017(2):29-34.
[9]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.
[10]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.
[11]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:中文版,2012,55(2):235-250.PEI H S,DENG W N.Naturally ordered transformation semigroups preserving order and an equivalence relation[J].Acta Mathematica Sicina:Chinese Series,2012,55(2):235-250.
[12]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):1 971-1 986.
[13]关艺,任苗苗,陈益智.双循环半群上的同余关系[J].纯粹数学与应用数学,2014,30(4):435-440.GUAN Y,REN M M,CHEN Y Z.Congruence relations on a bicyclic semigroup[J].Pure and Applied Mathematics,2014,30(4):435-440.
[14]徐波,赵平.半群POn的极大子半带[J].吉林大学学报:理学版,2012,50(3):445-451.XU B,ZHAO P.Maximal subsemibands of the semigroup POn[J].Journal of Jilin University:Science Edition,2012,50(3):445-451.
[15]金久林,郭桂容,游泰杰.双循环半群的极大逆子半群[J].吉林大学学报:理学版,2017,55(2):211-215.JIN J L,GUO G R,YOU T J.Maximal inverse subsemigroups of bicyclic semigroup[J].Journal of Jilin University:Science Edition,2017,55(2):211-215.
[16]WU J P,ZHANG R H.λ-semidirect products of regular orthodox semigroups[J].Journal of Yunnan University:Natural Sciences Edition,2003,25(6):469-473.
[17]张荣华,李秀妮.关于弱p-正则半群的一个注记[J].云南大学学报:自然科学版,2000,22(2):85-86.ZHANG R H,LI X N.A note on weakly p-regular semigroups[J].Journal of Yunnan University:Natural Sciences Edition,2000,22(2):85-86.
[2]PETRICH M.Inverse semigroups[M].New York:Wiley-Interscience,1984.
[3]SHANG Y,WANG L M.A class of regular simpleω2-semigroups-I[J].Advances in Mathematics(China),2013,42:631-643.
[4]SHANG Y,WANG L M,FENG Y Y.A class of regular simpleω2-semigroups-II[J].Communications in Mathematical Research,2013,29(4):351-362.
[5]CHEN H,HUANG H,GUO X J.On q*-bisimple IC semigroups of type E[J].Semigroup Forum,2009,78(1):106-117.
[6]GUO X J,SHUM.K.P.On translational hulls of type-A semigroups[J].J Algebra,2003,269(1):240-249.
[7]SHUM K P,DU L,GUO Y Q.Green's relations and their generalizations on semigroups[J].Discuss Math Gen Algebra Appl,2010,30(1):71-89.
[8]秦美青.保等价关系变换半群的变种半群上的自然偏序[J].华东师范大学学报:自然科学版,2017(2):29-34.QIN M Q.Natural order on variant semigroup of transformation semigroup preserving equivalence relation[J].Journal of East China Normal University:Natural Sciences Edition,2017(2):29-34.
[9]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.
[10]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.
[11]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:中文版,2012,55(2):235-250.PEI H S,DENG W N.Naturally ordered transformation semigroups preserving order and an equivalence relation[J].Acta Mathematica Sicina:Chinese Series,2012,55(2):235-250.
[12]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):1 971-1 986.
[13]关艺,任苗苗,陈益智.双循环半群上的同余关系[J].纯粹数学与应用数学,2014,30(4):435-440.GUAN Y,REN M M,CHEN Y Z.Congruence relations on a bicyclic semigroup[J].Pure and Applied Mathematics,2014,30(4):435-440.
[14]徐波,赵平.半群POn的极大子半带[J].吉林大学学报:理学版,2012,50(3):445-451.XU B,ZHAO P.Maximal subsemibands of the semigroup POn[J].Journal of Jilin University:Science Edition,2012,50(3):445-451.
[15]金久林,郭桂容,游泰杰.双循环半群的极大逆子半群[J].吉林大学学报:理学版,2017,55(2):211-215.JIN J L,GUO G R,YOU T J.Maximal inverse subsemigroups of bicyclic semigroup[J].Journal of Jilin University:Science Edition,2017,55(2):211-215.
[16]WU J P,ZHANG R H.λ-semidirect products of regular orthodox semigroups[J].Journal of Yunnan University:Natural Sciences Edition,2003,25(6):469-473.
[17]张荣华,李秀妮.关于弱p-正则半群的一个注记[J].云南大学学报:自然科学版,2000,22(2):85-86.ZHANG R H,LI X N.A note on weakly p-regular semigroups[J].Journal of Yunnan University:Natural Sciences Edition,2000,22(2):85-86.