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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Segment-preserving maps of partial orders

Author: Geert Prins
Journal: Trans. Amer. Math. Soc. 166 (1972), 351-360
MSC: Primary 06A10
MathSciNet review: 0291028
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Abstract: A bijective map from a partial order P to a partial order Q is defined to be segment-preserving if the image of every segment in P is a segment in Q. It is proved that a partial order P with 0-element admits nontrivial segment-preserving maps if and only if P is decomposable in a certain sense. By introducing the concept of ``strong'' segment-preserving maps further insight into the relations between segment-preserving maps and decompositions of partial orders is obtained.

References [Enhancements On Off] (What's this?)

  • [1] G. Birkhoff, Lattice theory, Amer. Math. Soc. Colloq. Publ., vol. 25, Amer. Math. Soc., Providence, R. I., 1940; 2nd rev. ed., 1948; 3rd ed., 1967. MR 1, 325; MR 10, 673; MR 37 #2638.

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Keywords: Segment-preserving map (bijection) of partial order, semidecomposition, semiproducts of partial orders
Article copyright: © Copyright 1972 American Mathematical Society