Covers in Free Lattices

Ralph Freese, J. B. Nation
1985 Transactions of the American Mathematical Society  
In this paper we study the covering relation ( u > v ) in finitely generated free lattices. The basic result is an algorithm which, given an element w e FL( X), finds all the elements which cover or are covered by w (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 FL( X) are classified;
more » ... e classified; again, with finitely many exceptions, they are all one-, two-or three-element chains.
doi:10.2307/2000423 fatcat:vg7dvk5pcvgezekj3htlvedqnu