完全J°-单半群的平移壳
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摘要
目的为给出完全J°-单半群的平移壳的结构。方法从完全J°-单半群的正规Rees矩阵半群结构出发构造其平移壳结构。结果给出了一个完全J°-单半群的平移壳的结构定理。结论所给出的结构定理是完全J*-单半群和完全单半群的平移壳结构定理的共同推广。
Aim In order to study the translational hulls of completely J°-simple semigroups.Methods The translational hulls of completely J°-simple semigroups are constructed by the corresponding normalized Rees matrix semigroup.Results A structure theorem of the translational hulls of completely J°-simple semigroups is given.Conclusion The main result in this paper is a generalization of the structure theorems of the translational hulls of completely J *-simple semigroups and completely simple semigroups.
Aim In order to study the translational hulls of completely J°-simple semigroups.Methods The translational hulls of completely J°-simple semigroups are constructed by the corresponding normalized Rees matrix semigroup.Results A structure theorem of the translational hulls of completely J°-simple semigroups is given.Conclusion The main result in this paper is a generalization of the structure theorems of the translational hulls of completely J *-simple semigroups and completely simple semigroups.
引文
[1]陈益智,李勇华.完全Jo-单半群的平移壳[J].华南师范大学学报:自然科学版,2007(1):28-31.
[2]FOUNTAIN J B,LAWSON M V.The translational hullof an adequte semigroup[J].Semigroup Forum,1985,32:79-86.
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[7]PETRICH M.Introduction to Semigroups[M].Colum-bus:Merrill,1973.
[8]PETRICH M.Inverse Semigroups[M].New York:Wileyand Sons Inc,1984.
[9]PETRICH M.The structure of completely regular semig-roups[J].Trans Amer Math Soc,1974,189:211-236.
[10]PETRICH M.The translational hull in semigroups andrings[J].Semigroup Forum,1970,1:283-360.
[11]PETRICH M,REILLY N.Completely Regular Semigroups[M].New York:Wiley and Sons Inc,1999.
[12]MCALISTER D B.One-to-one partial right translation of aright cancellative semigroup[J].J Algebra,1976,43:231-251.
[13]PASTIJN F.A representation of a semigroup by a semig-roup of matrices over a group with zero[J].Semigroup Fo-rum 1975,10:238-249.
[14]FOUNTAIN J B.Abundant semigroups[J].Proc LondonMath Soc,1982,44(3):103-129.
[15]CLIFFORD A H,PETRICH M.Some classes of complete-ly regular semigroups[J].J Algebra,1977,46:462-480.
[16]邱传林.格林o-关系和o-富足半群[D].广州:华南师范大学,2009.
[17]REN X M,SHUM K P.The structure of superabundantsemigroups[J].Science in China Ser A Math,2004.47(5):756-771.
[2]FOUNTAIN J B,LAWSON M V.The translational hullof an adequte semigroup[J].Semigroup Forum,1985,32:79-86.
[3]HOWIE J M.Fundamentals of Semigroup Theory[M].Oxford:Clarendon Press,1995.
[4]GUO X J,SHUM K P.On translationsal hulls of type asemigroups[J].J Algebra,2003,269:240-249.
[5]GUO X J,GUO Y Q.The translationsl hull of a stronglyright type a semigroup[J].Science in China,Ser A,Math,2000,43(1):6-12.
[6]LAWSON M V.The structure of type a semigroups[J].Quart J Math Soc,1982,44(3):103-129.
[7]PETRICH M.Introduction to Semigroups[M].Colum-bus:Merrill,1973.
[8]PETRICH M.Inverse Semigroups[M].New York:Wileyand Sons Inc,1984.
[9]PETRICH M.The structure of completely regular semig-roups[J].Trans Amer Math Soc,1974,189:211-236.
[10]PETRICH M.The translational hull in semigroups andrings[J].Semigroup Forum,1970,1:283-360.
[11]PETRICH M,REILLY N.Completely Regular Semigroups[M].New York:Wiley and Sons Inc,1999.
[12]MCALISTER D B.One-to-one partial right translation of aright cancellative semigroup[J].J Algebra,1976,43:231-251.
[13]PASTIJN F.A representation of a semigroup by a semig-roup of matrices over a group with zero[J].Semigroup Fo-rum 1975,10:238-249.
[14]FOUNTAIN J B.Abundant semigroups[J].Proc LondonMath Soc,1982,44(3):103-129.
[15]CLIFFORD A H,PETRICH M.Some classes of complete-ly regular semigroups[J].J Algebra,1977,46:462-480.
[16]邱传林.格林o-关系和o-富足半群[D].广州:华南师范大学,2009.
[17]REN X M,SHUM K P.The structure of superabundantsemigroups[J].Science in China Ser A Math,2004.47(5):756-771.