π-正则半群上的弱自然偏序关系与应用

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1、曲阜师范大学硕士学位毕业论文AbstractAfterestablishingthedefinationoftheweaknaturalorderof'r-regularsemigroup．weinvestigatetherelatedcharacterofkindsof”一regularsemigroup．Thisdissertationconsistsof8sections．Thefirsttwosectionsaxeintroductionandpreliminariesrespectively．Afterintroducingthebas

2、icdefinationsrelated，wegivethedefinationoftheweaknat-uralorderof丌-regularsemigroup：Va，b∈S，a!b甘a≤b甘a=eb=b／，(e，，∈E(s))．Inthethirdsection，weinvestigatemanycharacterofIt-regularsemigroupwiththedefinationoftheweaknaturalorder．Wedefinethemajorization，mi-norization，coveringandinvest

3、igatetherelatedcharacter．GV-semigroupisinvestigatedinsection4．Afterdefiningtheretractofsemi·groupandretractideal，combiningwithmajorizationandminorization，wein-vestigatetherelatedcharacterofthedefinationoftheweaknaturalorderweargued．Lemma4．4(2)Seta∈．％，n≥卢，then：3b∈函，SOthata三b．T

4、his1elTD：naofferbasicforthe1atertheoremofthestructureofnormal'r-cryptogroupinsection7．Thefifthsectiongivestheexpressionoftheweaknaturalorderonstrong71"--inversesemigroupandinvestigatesmanycharactersofthatsemigroup．Thecharactersof7r—eryptogroupandnormal"一cryptogroupareinvesti-

5、gatedinsection6and7．Inthe7thsection．athedefinationofsimilarclassasfollow：Wename＆asthesimilarclasswhicholiesin，ifVa，b∈乳，s．ta=b，thatisa2b，Theorem7．7Normal”一cryptogroupistheclassstrongsemilatticeofcompletelyachimedeansemigroup．Itgivesthestructuretheoremofnormal7r—cryptogroup：Ano

6、rmalⅡ一crypto曲卓师范大学硕士学位毕业论文groupSisclassstrongsemilatticeofcompletelyarchimedeansemigroup，whichwenamedclassstrongsemilattice-In8ection8，wedefinethe"一orthogroupandinvestigateitschatacters·Keywords7r—regularsemigroup；weaknaturalorder；strongGV—semigroup；玎一cryptogroup；normal7r—cry

7、ptogroup；7r—orthogroup；81mila。cJa8s；classstrongsemilattice曲阜师范大学硕士学位毕业论文§l引言半群理论作为代数领域的一个分支，自从Sushkevich的<>出版之后．在包括M·Howie、H·Clifford、M·Petrich、S·Bogdanovic在内的众多伟大数学家的不懈努力下，半群的研究体系不断扩大，不仅涵盖了最基本的单半群、正则半群、完全正则半群、逆半群、纯正半群、带以及各种半群的同余和簇等方面，而且还出现了比如断面、E

8、一反演半群、富足半群、双序集、阿基米德半群、”一正则半群、GV一半群等一系列新的概念和相关研究方法，，研究体系和方法精密严谨，理论性极强