Lattices isomorphic with their free powers
The author solves two problems (VI. 6 and VI. 7) from the reviewer's ''General lattice theory'' (1978; Zbl 0385.06015): There exist two lattices A, B such that A*A\(\cong B*B\) but \(A\cong \!/B\). There exist lattices A, B, C such that A*A*C\(\cong B*B*C\) but A*C\(\cong \!/B*C\). Both of these results follow from the following Theorem. For every \(N\geq 3\), there exists a lattice L such that L is isomorphic to the free product of N copies of L but not to the free product of K copies of L for any \(K<N\). The proof is ingenious, deep, but somewhat cryptic.
scientific article; zbMATH DE number 3912435