| The Semimodularity of Cardinal Power of Posets |
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| 作者姓名： | 胡长流 |
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| 作者单位： | Department of Mathematics，Henan University |
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| 摘 要： | LetX,Ybeanyposets,Y'denotethecardinalpowerwithbaseYandexponentX.Fortherelatedconceptslsymbolsorterminologies,seeF1],2jor3].lnL1],someexamplesaregaven,whichshowthatthesemimodularityofX,YandYxareindepentent.AndaquestionisaskedthatwhenthecardinalpowerYxwithbaseYandexpo-nentXissemimodular.Wenowanswerthequestioninthispaper.LemmaLetX,Ybeanyposets,f,geyx,thenthefollowingconditionsareequivalent:(l)fiscoveredbyg(denotedbyf,g);(2)Thereexists'anelementxoeX,suchthatf(x,),g(x,),andf(x)=g(x)(foran…
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| 关 键 词： | 偏序集 基数幂 半模性 |
The Semimodularity of Cardinal Power of Posets |
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| Hu Changliu.The Semimodularity of Cardinal Power of Posets[J].Chinese Quarterly Journal of Mathematics,1997,12(1):47-51. |
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| Authors: | Hu Changliu |
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| Abstract: | Let X,Y be any posets,the semimodularity of cardinal power Yx with base Y and exponent X is studied. Some necessary or sufficient conditions for Yx to be semimodular are gaven, |
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| Keywords: | poset cardinal power of posets seimodularity |
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