| The Minimun -Bases for Partially Order Sets |
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| 引用本文： | 金晨辉,林志周,黄堃.The Minimun -Bases for Partially Order Sets[J].东北数学,1999(3). |
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| 作者姓名： | 金晨辉 林志周 黄堃 |
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| 作者单位： | Jin Chenhui(2nd Department，Zhengzhou Electronic Technology University，Zhengzhou，450004)Lin Zhizhou(Department of Basic Science，Henan Textile College，Zhengzhon，450007)Huang Kun(Department of Mithematics，Pingdingshan Normal College，Pingdingshan. Hen |
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| 摘 要： | Asetofgeneratingelements(see1,2J)anditsdualconcept,anordergeneratingset(seeL3]),areimportantconceptsinlatticetheory.Theconceptofasetofgeneratingelementforcontlnuouspartiallyordersetswasalsoproposedin2J-Inthispaper,theconceptofageneratingsystemisintroducedatfirst-ThentheconceptofpbaseforthegeneratingsystemFofapartiallyorderset(P0Sforshort)isprop0sed-Finally,theminimumpbasesf0rPOSarestudied.Definition1LetTbeasetofsubsetsofaPOSL.Iff0ranyaeL,thereexistsAep,suchthata=supA,then9iscalledage…
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| 关 键 词： | Partially Order Set Generating System ■-base Sup-complete Partially Order Set Compact Element |
The Minimun Bases for Partially Order Sets |
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| Jin Chenhui.The Minimun Bases for Partially Order Sets[J].Northeastern Mathematical Journal,1999(3). |
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| Authors: | Jin Chenhui |
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| Abstract: | In this paper, the authors propose the concept of pbase for partially order sets,give a necessary and sufficient condition under which a partially order set with a complete generating system has a minimum base, and prove that the minimum base is composed of all completely sup-irreducible elements. The authors also study the structures of the minimum bases for generating systems pone often meets. Finally, the authors prove that a partially order set has the least base if its dual partially order set is sup-complete and each element in which is a supremum of compact elements, and hence the dual partially order set of an algebraic partially order set has the least base. |
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