LATTICE TENSOR PRODUCTS. II.
Ideal Lattices · 2000
G. Gratzer and F. Wehrung has recently introduced the lattice tensor product, A B, of the lattices A and B. In this note, for a finite lattice A and an arbitrary lattice B, we compute the ideal lattice of A B, obtaining the isomorphism Id(A B) ∼ A Id B. This generalizes an earlier result of G. Gratzer and F. Wehrung proving this isomorphism for A = M3 and Bn -modular. We prove this isomorphism by utilizing the coordinatization of A B in- troduced in Part I of this paper.