Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Segment-preserving maps of partial orders
HTML articles powered by AMS MathViewer

by Geert Prins PDF
Trans. Amer. Math. Soc. 166 (1972), 351-360 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.
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 06A10
  • Retrieve articles in all journals with MSC: 06A10
Additional 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