Covers in free lattices

Authors:
Ralph Freese and J. B. Nation

Journal:
Trans. Amer. Math. Soc. **288** (1985), 1-42

MSC:
Primary 06B25

DOI:
https://doi.org/10.1090/S0002-9947-1985-0773044-4

MathSciNet review:
773044

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Abstract: In this paper we study the covering relation in finitely generated free lattices. The basic result is an algorithm which, given an element , finds all the elements which cover or are covered by (if any such elements exist). Using this, it is shown that covering chains in free lattices have at most five elements; in fact, all but finitely many covering chains in each free lattice contain at most three elements. Similarly, all finite intervals in are classified; again, with finitely many exceptions, they are all one-, two- or three-element chains.

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DOI:
https://doi.org/10.1090/S0002-9947-1985-0773044-4

Article copyright:
© Copyright 1985
American Mathematical Society