关于E-酉逆半群和E-自反逆半群的若干研究
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摘要
本文研究E-酉逆半群和E-自反逆半群
第一部分是预备知识。
第二部分对双循环半群进行了推广,定义了一种n循环半群,通过分析其运算给出了其自然表示,证明了该n循环半群不是双单的,并且只有含幂等元的那个D-类是正则的。
第三部分对多循环半群进行了研究,讨论了多循环半群的置换性质,证明了当n≥3时,多循环半群有置换性质(?)_n。
第四部分用对偶准同态刻划了E-自反逆半群。
In this paper,the concepts of E-unitary inverse semigroups and E-reflexive inverse semigroups are introduced.
In the first part,basic knowledge is introduced.
In the second part,bicyclic semigroups are studied,as a generalization of bicyclic semigroups;a kind of n-cyclic semigroup is defined.By analyzing the multiplication, its natural representations are given.We proved that the n-cyclic semigroup is not bisimple,and only the D-class containing idempotents is regular.
In the third part,polycyclic semigroups are studied,the permutation property of the polycyclic semigroups has been discussed,and the results have shown polycyclic semigroup has permutation property(?)_n,n≥3.
In the fourth part,E-reflexive inverse semigroups are characterized in terms of dual-prehomomorphisms.
第一部分是预备知识。
第二部分对双循环半群进行了推广,定义了一种n循环半群,通过分析其运算给出了其自然表示,证明了该n循环半群不是双单的,并且只有含幂等元的那个D-类是正则的。
第三部分对多循环半群进行了研究,讨论了多循环半群的置换性质,证明了当n≥3时,多循环半群有置换性质(?)_n。
第四部分用对偶准同态刻划了E-自反逆半群。
In this paper,the concepts of E-unitary inverse semigroups and E-reflexive inverse semigroups are introduced.
In the first part,basic knowledge is introduced.
In the second part,bicyclic semigroups are studied,as a generalization of bicyclic semigroups;a kind of n-cyclic semigroup is defined.By analyzing the multiplication, its natural representations are given.We proved that the n-cyclic semigroup is not bisimple,and only the D-class containing idempotents is regular.
In the third part,polycyclic semigroups are studied,the permutation property of the polycyclic semigroups has been discussed,and the results have shown polycyclic semigroup has permutation property(?)_n,n≥3.
In the fourth part,E-reflexive inverse semigroups are characterized in terms of dual-prehomomorphisms.
引文
[1]McAlister D.B.Groups,semilattices and inverse semigroups.Trans.Amer.Math.Soc.,19?4,(192):227-244
[2]O'Carrol L.Embedding theorems for proper inverse semigroups.J.Algebra,1976,(42):26-40
[3]Szendrdi M.B.E-unitarg R-unipotent semigroups.Semigroup Forum,1985,(32):87-96
[4]Szendrdi M.B.A generalization of McAlisters P-theorem for E-unitarg Regular Semigroups.Acta.Sci.Math.,1987,(51):229-249
[5]Imaoka T,Yokoyama H,Inata I.Some remarks on E-unitarg Regular *-Semigroups.Algebra Colloq.,1996,3(2):117-124
[6]李勇华.E-酉正则半群.数学学报,2005,48(3):577-584
[7]LI Yong Hua.On E-Unitary Regular Semigroups.Acta.Math.Sinica,2002,18(3):565-578
[8]McAlister D.B,Reilly N R.E-unitary covers for inverse semigroups.Pacific J.Math.,1977,(68):161-174
[9]郭小江.纯正Bruck半群的E-酉覆盖.数学杂志,1999,19(2):167-170
[10]陈历敏.0-范畴E~*-酉逆半群的结构.数学理论与应用,2004,24(1):72-79
[11]陈历敏.一类逆半群的嵌入定理.数学的实践与认识,2006,36(3):257-260
[12]O'Carrol L.Strongly E-reflexive inverse semigroups.Proceedings Malhematical Sociaty,1978,(21):1-10
[13]黄天霖.E-自反逆半群的一个结构定理.西南师范大学学报(自然科学版),1995,20(2):125-131
[14]黄天霖,曹聪.E-自反逆半群的嵌入定理.兰州大学学报(自然科学版),1995,31(3):24-29
[15]黄天霖.E-自反逆半群上的群同余.兰州大学学报(自然科学版),2005,41(5):113-116
[16]黄天霖.E-自反逆半群上的Clifford同余.纯粹数学与应用数学,2005,21(3):255-262
[17]蒋启芬,喻秉均.一类广义双循环半群.四川师范大学学报(自然科学版),1999,22(1):17-23
[18]周淑云.双循环半群同余的刻划.青海师专学报(教育科学),2005,(4):8-10
[19]朱用文.一类三循环半群.烟台大学学报(自然科学与工程版),2006,19(3):166-169
[20]石永芳.毕竟纯整半群上的逆半群同余:[兰州大学硕士学位论文].兰州:兰州 大学数学系,2004,1-17
[21]Howie J.M.Fundamentals of Semigroup Theory.Berlin:John Wiley and Sons,Academic-Verlag,1977,13-199
[22]Howie J.M.Congruences and Green's relations on regular semigroups.Glasgow Math.J.,1972,(13):167-175
[23]李小玲.E-逆半群上的一类特殊同余.兰州理工大学学报,2006,32(3):155-156
[24]Lawson M.V.Inverse Semigroup.London:World Scientific Publishing Co.Pte.Ltd.,1998,21-291
[25]郭子胥.E-酉的逆半群.陕西师范大学学报,2002,(5):12-15
[26]郭子胥.子半群与子酉半群.青海师范大学学报(自然科学版),2002,(4):7-9
[27]Chen Li-min.A Note on O-F-inverse Semigroup.Chin.Quart.J.of Math,2006,21(2):252-254
[28]S.Bulman-Fleming,J.Fountain,V.Gould.Inverse semigroups with zero:covers and their structure.J.Austral Math.Soc,Series A,1999(67):15-30
[29]Lawson M.V.Inverse Semigroups:The theory of partial symmetries.Singapore.World-Scientific,1998
[30]Wilkinson R.A description of E-Unitarg inverse semigroups,proc of the Royal society of Edinburgh,1983(95A):239-242
[31]张谋成,李勇华.正则半群的幂等元同余类.华南师范大学学报(自然科学版),1995,(4):57-60
[32]Hines P.M.and Lawson M.V.An Application of Polycyclic Monoids to Rings.Semigroup Forum,1998,(56):146-149
[33]周林芳,李宝.双循环半群的置换性质.兰州大学学报(自然科学版),2000,36(2):1-5
[34]ANDRZEJ K.Permutation class of a semigroup.Journal of Algebra,2002,(26):295-310
[35]Kelarev A.V.On the weak permutation property.Semigroup Forum,1994,(48):253-254
[36]李伟霞,石玉华.一般半群上的群的半格同余.山东师范大学学报(自然科学版),2004,19(1):77-78
[37]石永芳,李小玲.毕竟正则半群上的群同余.兰州大学学报(自然科学版),2005,41(5):117-119
[38]李小玲.正则半群上的完全单半群同余.兰州大学学报(自然科学版),2006,42(2):96-98
[39]Chen Li-min.A Representation Theorem for E'-unitary Categorical Inverse Semigroups.Advances in Mathematics, 2006, 35(2):244-248
[40]Lawson M. V. The structure of 0- E-unitarg inverse semigroups. The monoid Case, Proc. the Edinburgh Math. Society,1999, 42(3):497-520
[41]Chen Li-min.Structure of E~(?)-unitary Categorical Inverse Semigroups.J. Math. Research and Exposition,2006, 26(2):239-246
[2]O'Carrol L.Embedding theorems for proper inverse semigroups.J.Algebra,1976,(42):26-40
[3]Szendrdi M.B.E-unitarg R-unipotent semigroups.Semigroup Forum,1985,(32):87-96
[4]Szendrdi M.B.A generalization of McAlisters P-theorem for E-unitarg Regular Semigroups.Acta.Sci.Math.,1987,(51):229-249
[5]Imaoka T,Yokoyama H,Inata I.Some remarks on E-unitarg Regular *-Semigroups.Algebra Colloq.,1996,3(2):117-124
[6]李勇华.E-酉正则半群.数学学报,2005,48(3):577-584
[7]LI Yong Hua.On E-Unitary Regular Semigroups.Acta.Math.Sinica,2002,18(3):565-578
[8]McAlister D.B,Reilly N R.E-unitary covers for inverse semigroups.Pacific J.Math.,1977,(68):161-174
[9]郭小江.纯正Bruck半群的E-酉覆盖.数学杂志,1999,19(2):167-170
[10]陈历敏.0-范畴E~*-酉逆半群的结构.数学理论与应用,2004,24(1):72-79
[11]陈历敏.一类逆半群的嵌入定理.数学的实践与认识,2006,36(3):257-260
[12]O'Carrol L.Strongly E-reflexive inverse semigroups.Proceedings Malhematical Sociaty,1978,(21):1-10
[13]黄天霖.E-自反逆半群的一个结构定理.西南师范大学学报(自然科学版),1995,20(2):125-131
[14]黄天霖,曹聪.E-自反逆半群的嵌入定理.兰州大学学报(自然科学版),1995,31(3):24-29
[15]黄天霖.E-自反逆半群上的群同余.兰州大学学报(自然科学版),2005,41(5):113-116
[16]黄天霖.E-自反逆半群上的Clifford同余.纯粹数学与应用数学,2005,21(3):255-262
[17]蒋启芬,喻秉均.一类广义双循环半群.四川师范大学学报(自然科学版),1999,22(1):17-23
[18]周淑云.双循环半群同余的刻划.青海师专学报(教育科学),2005,(4):8-10
[19]朱用文.一类三循环半群.烟台大学学报(自然科学与工程版),2006,19(3):166-169
[20]石永芳.毕竟纯整半群上的逆半群同余:[兰州大学硕士学位论文].兰州:兰州 大学数学系,2004,1-17
[21]Howie J.M.Fundamentals of Semigroup Theory.Berlin:John Wiley and Sons,Academic-Verlag,1977,13-199
[22]Howie J.M.Congruences and Green's relations on regular semigroups.Glasgow Math.J.,1972,(13):167-175
[23]李小玲.E-逆半群上的一类特殊同余.兰州理工大学学报,2006,32(3):155-156
[24]Lawson M.V.Inverse Semigroup.London:World Scientific Publishing Co.Pte.Ltd.,1998,21-291
[25]郭子胥.E-酉的逆半群.陕西师范大学学报,2002,(5):12-15
[26]郭子胥.子半群与子酉半群.青海师范大学学报(自然科学版),2002,(4):7-9
[27]Chen Li-min.A Note on O-F-inverse Semigroup.Chin.Quart.J.of Math,2006,21(2):252-254
[28]S.Bulman-Fleming,J.Fountain,V.Gould.Inverse semigroups with zero:covers and their structure.J.Austral Math.Soc,Series A,1999(67):15-30
[29]Lawson M.V.Inverse Semigroups:The theory of partial symmetries.Singapore.World-Scientific,1998
[30]Wilkinson R.A description of E-Unitarg inverse semigroups,proc of the Royal society of Edinburgh,1983(95A):239-242
[31]张谋成,李勇华.正则半群的幂等元同余类.华南师范大学学报(自然科学版),1995,(4):57-60
[32]Hines P.M.and Lawson M.V.An Application of Polycyclic Monoids to Rings.Semigroup Forum,1998,(56):146-149
[33]周林芳,李宝.双循环半群的置换性质.兰州大学学报(自然科学版),2000,36(2):1-5
[34]ANDRZEJ K.Permutation class of a semigroup.Journal of Algebra,2002,(26):295-310
[35]Kelarev A.V.On the weak permutation property.Semigroup Forum,1994,(48):253-254
[36]李伟霞,石玉华.一般半群上的群的半格同余.山东师范大学学报(自然科学版),2004,19(1):77-78
[37]石永芳,李小玲.毕竟正则半群上的群同余.兰州大学学报(自然科学版),2005,41(5):117-119
[38]李小玲.正则半群上的完全单半群同余.兰州大学学报(自然科学版),2006,42(2):96-98
[39]Chen Li-min.A Representation Theorem for E'-unitary Categorical Inverse Semigroups.Advances in Mathematics, 2006, 35(2):244-248
[40]Lawson M. V. The structure of 0- E-unitarg inverse semigroups. The monoid Case, Proc. the Edinburgh Math. Society,1999, 42(3):497-520
[41]Chen Li-min.Structure of E~(?)-unitary Categorical Inverse Semigroups.J. Math. Research and Exposition,2006, 26(2):239-246