Lattices isomorphic with their free powers
type: Item
instance of: scholarly article
title: Lattices isomorphic with their free powers
zbMATH Open document ID: 0572.06004
DOI: 10.1007/BF00337925
published in: Order
publication date: 1985-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 06B05
Mathematics Subject Classification ID: 06B25
zbMATH DE Number: 3912435
zbMATH Keywords: noncancellable lattices
zbMATH Keywords: free product
author: Jaroslav Ježek
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00337925
OpenAlex ID: W2124789433
description: scientific article; zbMATH DE number 3912435