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1、Rees超同余论文：半群超结构理论的若干研究【中文摘要】在超半群代数理论的发展过程中,模糊超同余和模糊超理想起着越来越重要的作用。很多时候,我们常通过研究其上的模糊同余和模糊理想,由此获得超半群的内部结构及其同态像等知识。本文主要研究在超半群上定义的Rees超同余、模糊Rees超同余,以及对Davvaz在中阐述的同构理论进行推广；同时我们介绍了在超半群上定义的模糊广义理想,借助模糊左超理想、模糊右超理想、模糊(广义)超双理想来研究正则超半群的性质。本文借助模糊集理论实现了从半群或序半群到超半群的平移。第一章介绍了论文的背景及所涉及的基本概念。第二章在模糊半群上定义的Rees同余的概念,
2、我们研究了超半群上定义的Rees超同余和模糊Rees超同余,同时介绍了模糊Rees弱超半群以及模糊Rees弱超半群上定义的超同余及其性质。第三章介绍了超半群的模糊广义理想,借助模糊左超理想、模糊右超理想、模糊(广义)超双理想来研究正则超半群的性质。【英文摘要】Fuzzyhypercongruencerelationsandfuzzyhyperidealsplayanimportantroleinthepro-cessofhyperalgebraicstructures.Mostoftime,usingthesefuzzyhypercongruencerelationsandfuzzyh
3、yperideals,weobtainedthestructuresandpropertiesofhomomorphicimageofthehyperalgebraicstructures.Inthispaper,ReeshypercongruencesandfuzzyReeshypercongruencesonhypersemi-groupsarestudied.Moreover,wegeneralizeahomomorphismtheoremofDavvazin[5].Atthesametimeweintroducetheconceptofthefuzzygeneralizedhy
4、perbi-idealsofahypersemi-group,andregularhypersemigroupsarecharacterizedbymeansoffuzzylefthyperideals,fuzzyrighthyperidealsandfuzzy(generalized)hyperbi-ideals.Finally,wegivetwomaintheoremswhichcharacterizetheregularhypersemigroupsandintra-regularhypersemigroupsintermsoffuzzylefthyperideals,fuzzy
5、righthyperideals,fuzzyhyperbi-ideals,fuzzyhyperquasi-ideals.Thepapershowsthatonecanpassfromresultsintermsoffuzzysubsetsinsemigroupsororderedsemigroupstohypersemigroups.InChapterOne,weintroducethebackgroudofthisthesisandsomebasicconcepts.InChaptertwo,UsingtheconceptofReescongruencesonsemigroupsan
6、dfuzzysetspresentedbyZadeh,wehaveinvestigatedtheReeshypercongruencesandfuzzyReeshyper-congruencesonahypersemigroups,wealsointroducefuzzyReesweakhypercongruenceshy-persemigroupandgivecharacterizationsofhypercongruencesonFRWH-semigroups.InChapterthree,weintroducetheconceptofthefuzzygeneralizedhype
7、rbi-idealsofahypersemigroup,andregularhypersemigroupsarecharacterizedbymeansoffuzzylefthyper-ideals,fuzzyrighthyperidealsandfuzzy(generalized)hyperbi-ideals.Finally,wegivetwomaintheoremswhichcharacterizetheregularhypersemigr
