Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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SOME FAMILIES OF IDEAL-HOMOGENEOUS POSETS

  • Chae, Gab-Byung (Division of Mathematics and Informational Statistics Wonkwang University) ;
  • Cheong, Minseok (College of Information Information Security Convergence Korea University) ;
  • Kim, Sang-Mok (Department of Mathematics Kwangwoon University)
  • Received : 2015.03.20
  • Published : 2016.07.31
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Abstract

A partially ordered set P is ideal-homogeneous provided that for any ideals I and J, if $$I{\sim_=}_{\sigma}J$$, then there exists an automorphism ${\sigma}^*$ such that ${\sigma}^*{\mid}_I={\sigma}$. Behrendt [1] characterizes the ideal-homogeneous partially ordered sets of height 1. In this paper, we characterize the ideal-homogeneous partially ordered sets of height 2 and nd some families of ideal-homogeneous partially ordered sets.

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References

  1. G. Behrendt, Homogeneity in Finite Ordered Sets, Order 10 (1993), no. 1, 65-75. https://doi.org/10.1007/BF01108709
  2. B. A. Davey and H. A. Priestley, Introduction to Lattices and Order, Second edition, Cambridge University Press, 2002.