Residuated lattices do not have the amalgamation property
Rings and Algebras
2026-03-23 v2 Logic
Abstract
We show that the variety of residuated lattices does not have the amalgamation property, thereby settling a long-standing open problem. In addition, we show that the amalgamation property fails for several subvarieties, including idempotent residuated lattices, involutive residuated lattices, and (integral) distributive residuated lattices.
Cite
@article{arxiv.2504.16111,
title = {Residuated lattices do not have the amalgamation property},
author = {Peter Jipsen and Simon Santschi},
journal= {arXiv preprint arXiv:2504.16111},
year = {2026}
}
Comments
7 pages, 4 figures