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1、曲阜師范大學(xué)碩士學(xué)位畢業(yè)論文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≥盧，then：3b∈函，SOthata三b．T
4、his1elTD：naofferbasicforthe1atertheoremofthestructureofnormal'r-cryptogroupinsection7．Thefifthsectiongivestheexpressionoftheweaknaturalorderonstrong71"--inversesemigroupandinvestigatesmanycharactersofthatsemigroup．Thecharactersof7r—eryptogroupandnormal"一cryptogroupareinvesti-
5、gatedinsection6and7．Inthe7thsection．a(chǎn)thedefinationofsimilarclassasfollow：Wename＆asthesimilarclasswhicholiesin，ifVa，b∈乳，s．ta=b，thatisa2b，Theorem7．7Normal”一cryptogroupistheclassstrongsemilatticeofcompletelyachimedeansemigroup．Itgivesthestructuretheoremofnormal7r—cryptogroup：Ano
6、rmalⅡ一crypto曲卓師范大學(xué)碩士學(xué)位畢業(yè)論文groupSisclassstrongsemilatticeofcompletelyarchimedeansemigroup，whichwenamedclassstrongsemilattice-In8ection8，wedefinethe"一orthogroupandinvestigateitschatacters·Keywords7r—regularsemigroup；weaknaturalorder；strongGV—semigroup；玎一cryptogroup；normal7r—cry
7、ptogroup；7r—orthogroup；81mila。cJa8s；classstrongsemilattice曲阜師范大學(xué)碩士學(xué)位畢業(yè)論文§l引言半群理論作為代數(shù)領(lǐng)域的一個(gè)分支，自從Sushkevich的<>出版之后．在包括M·Howie、H·Clifford、M·Petrich、S·Bogdanovic在內(nèi)的眾多偉大數(shù)學(xué)家的不懈努力下，半群的研究體系不斷擴(kuò)大，不僅涵蓋了最基本的單半群、正則半群、完全正則半群、逆半群、純正半群、帶以及各種半群的同余和簇等方面，而且還出現(xiàn)了比如斷面、E
8、一反演半群、富足半群、雙序集、阿基米德半群、”一正則半群、GV一半群等一系列新的概念和相關(guān)研究方法，，研究體系和方法精密?chē)?yán)謹(jǐn)，理論性極強(qiáng)
