Free Lattices Generated by Partially Ordered Sets and Preserving Bounds
Richard A. Dean · Canadian Journal of Mathematics · 1964
A construction of the free lattice generated by a partially ordered set P and preserving every least upper bound (lub) and greatest lower bound (glb) of pairs of elements existing in P has been given by Dilworth (2, pp. 124-129) and, when P is finite, by Gluhov (5). The results presented here construct the free lattice FL generated by the partially ordered set P and preserving (1) the ordering of P (2) those lub's of a family of finite subsets of P which possess lub's in P