Isometrical Embeddings of Lattices into Geometric Lattices

摘要

A lattice is said to be finite height generated if it is complete and every element is the join of some elements of finite height. Extending former results by Gratzer and Kiss (Order 2:351-365, 1986) on finite lattices, we prove that every finite height generated algebraic lattice that has a pseudorank function is isometrically embeddable into a geometric lattice.