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

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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