Segment-preserving maps of partial orders
HTML articles powered by AMS MathViewer
- by Geert Prins
- Trans. Amer. Math. Soc. 166 (1972), 351-360
- DOI: https://doi.org/10.1090/S0002-9947-1972-0291028-0
- PDF | Request permission
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
- 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.
Bibliographic Information
- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 166 (1972), 351-360
- MSC: Primary 06A10
- DOI: https://doi.org/10.1090/S0002-9947-1972-0291028-0
- MathSciNet review: 0291028