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Discussiones Mathematicae General Algebra and Applications 22(1) (2002) 39-46
DOI: https://doi.org/10.7151/dmgaa.1046

POWER-ORDERED SETS

Martin R. Goldstern Technische Universität Wien Institut für Algebra und Computermathematik Wiedner Hauptstraße 8-10/118, A-1040 Wien, Austria e-mail: martin.goldstern@tuwien.ac.at http://www.tuwien.ac.at/goldstern/

Dietmar Schweigert FB Mathematik, Universität Kaiserslautern Postfach 3049, D-67653 Kaiserslautern, Germany e-mail: schweigert@mathematik.uni-kl.de http://www.mathematik.uni-kl.de/~schweige/

Abstract

We define a natural ordering on the power set  P(Q) of any finite partial order Q, and we characterize those partial orders Q for which  P(Q) is a distributive lattice under that ordering.

 Keywords: partial order, chain, linear order, antichain, power set, power-ordered set, distributive lattice, anti-automorphism.

 2000 AMS Mathematics Subject Classifications: 06A06, O6A10.

References

[1] J.C. Abbott, Sets, Lattices and Boolean Algebras, Allyn & Bacon, Inc., Boston, MA, 1969

[2] J. Naggers and H.S. Kim, Basic Posets, World Scientific Publ. Co., River Edge, NJ, 1998.

Received 29 January 2002