关于变换半群的若干结果

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1、山东师范大学硕士学位论文SomeResultsonTransformationSemigroupsLiuY．uchunTheInstituteofScienceofMathematics，ShandongNormalUniversity。Jinan，Shandong，250014，P．R．ChinaABSTRACTInthisdissertation，westudythenaturalpartialorderedOilorder-preservingtrans-formationsemigroups，naturallypartial

2、orderedonthesandwichransformationsemi-groupsprservinganequivalence，naturallypartialorderedonorder—preservingpartialtransformationsemigroupsandthepropertiesofidempotentsoforder-preservingpartialtransformationsemigroup．Inthefirstchapter，wemainlystudiesthenaturalpartialor

3、dered“5”ontheorder-preservingtransformationsemigroup．Wetalkaboutthemaximalelements，theminimalelementsandthecoveringelements．Themainresultsaregivenasfollows：Theorem1．2．3Thefollowingstatementsareequivalentfor(On，5)：(1)，5夕；(2)，=a夕and7r(9)refine7r(，)forsomeQ∈E(On)；(3)，=夕∥a

4、ndimf∈imgforsomep∈E(瓯)；(4)imf∈img，丌(9)refine7r(，)andifz9∈imfforeachz∈．)‰，thenx9=z，．Theorem1．3．2Let，∈DtI，then，ismaximalwithrespectto“5”ifandonlyifoneofthefollowingstatementshold：(1)，isconstant；(2)I(z一1)，一1l≤1，l(z+I)／一1lS1forsomeZ∈％＼iml．Inthesecondchapter，wemainlystudies

5、thenaturalpartialorderedonthesandwichransformationsemigroupsprservinganequivalence．Wetalkaboutthecompatibility,themaximalelementsandtheminimalelements．Themainresultsaregivenasfollows：Theorem2．2．1If，，9∈TE(X；p)，then，5gifandonlyifThefollowingstate-mentshold：(1)E(Og)refine

6、E(，)，7r(的)refine7r(趴(2)Foreachz∈X，ifOg(x)∈of(x)，thenof(x)=p夕(z)；(3)ForeachA∈X／E，thereexistsB∈X／Esuchthatf(A)∈fie(B)．Theorem2．3．2Let，，g∈TE(X；口)and，墨g．Ifh∈而僻；p)，hisbothregularandsurjective，也en，Oh冬夕Oh．Theorem2．3．5Let，，g∈TE(X；8)and，冬g．Ifh∈TE(X；口)，hisbothregular3山东师范大学硕士学位论

7、文andinjeetive，thenhO，5h09．Inthethirdchapter，wemainlystudiesthenaturalpartialorderedontheorder-preservingpartialtransformationsemigroupPE(x)．Wetalkaboutthecompatibility,themaximalelements，theminimalelementsandthecoveringelements．Themainresultsaregivenasfollows：’Theorem3

8、．2．1Letf，g∈您(x)，thenf5gifandonlyifThefollowingstate-mentshold：(1)E(g)ndomfrefineE(，)，7r(夕)ndomfrefine7r(，)；(2)Foreach