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arXiv · 2504.16111

Residuated lattices do not have the amalgamation property

Peter Jipsen·Simon Santschi
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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.

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Peter Jipsen, Simon Santschi. 2025-04-17. Residuated lattices do not have the amalgamation property. https://arxiv.org/abs/2504.16111

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