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半连续格上的一个注记 被引量:15

A Note on Semicotinuous Lattices
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摘要 就文献[3]中的命题4.7提供了一种简单证法。此外,我们给出了在半连续格条件下伪素元的内部刻画。最后,我们定义了一种新的元素——弱素元,给出了伪素元,■-素元与弱素元等价的条件。 In this paper we provide a simple solution with Proposition 4.7 in [3]. In addition, we give the intrinsic characterization of pseudo prime elements in a semicontinuous lattice. Finally, notion of weak prime elements is introduced and the condition for the equality between pseudo prime elements, 〈=-prime elements and weak prime elements is given.
作者 姜广浩
机构地区 南京大学数学系
出处 《模糊系统与数学》 CSCD 北大核心 2008年第1期15-17,共3页 Fuzzy Systems and Mathematics
关键词 半连续格 伪素元 〈=-素元 弱素元 Semicontinuous Lattices Pseudoprime Elements 〈=-prime Elements Weak Prime Elements
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参考文献4

  • 1Gierz G,et al. Continuous lattices and domains[M]. Cambrige University Press,2003.
  • 2Ray Y. Semiprime ideals in general lattices [J].Pure and Applied Algebra, 1989, 56:105-118.
  • 3伍秀华,李庆国,许任飞.半连续格的性质[J].模糊系统与数学,2006,20(4):42-46. 被引量:12
  • 4Zhao D. Semicontinuous lattices[J]. Algebraic Unlversalis, 1997,37. 458-476.

二级参考文献6

  • 1Scott D S.Continuous lattices[A].In Topos,Algebraic Geometry and Logic,Lecture Notes in Math(Vol 274)[C].Berlin,New York:Springer-Verlag,1972.
  • 2Zhao D.Semicotinuous lattice[J].Algebraic Universalis,1997,37:458~476.
  • 3Liu Y M,Liang J H.Solutions to two problems of J.D.Lawson and M.Mislove[J].Topology and Its Applied,1996,69:153~164.
  • 4Ray Y.Semiprime ideals in general lattices[J].J.Pure and Applied Algebra,1989,56:105~118.
  • 5Gierz G,et al.Continuous lattices and domains[J].Cambridge University Press,2003.
  • 6寇辉,刘应明.Smyth幂半格及其连续domain表示[J].数学学报(中文版),2002,45(2):209-214. 被引量:4

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