Residuated lattices do not have the amalgamation property
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917354389110784 |
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| author | Jipsen, Peter Santschi, Simon |
| author_facet | Jipsen, Peter Santschi, Simon |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_16111 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Residuated lattices do not have the amalgamation property Jipsen, Peter Santschi, Simon Rings and Algebras Logic 06F05, 03G25, 03B47 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. |
| title | Residuated lattices do not have the amalgamation property |
| topic | Rings and Algebras Logic 06F05, 03G25, 03B47 |
| url | https://arxiv.org/abs/2504.16111 |