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

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.

Acknowledgement

Supported by : Wonkwang University

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.