The pairwise distributive law of semilattice congruences
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915592309571584 |
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| author | Martin-Maroto, Fernando Ricciardo, Antonio de Polavieja, Gonzalo G. |
| author_facet | Martin-Maroto, Fernando Ricciardo, Antonio de Polavieja, Gonzalo G. |
| contents | We show that the congruence lattice of a semilattice satsifies a form of distributivity relative to principal congruences of the form $ Θ_{t \odot s, s}$. Particularly, we establish that semilattice congruences obey the ``pairwise distributive law": \[ (\cap_{i \in w} Ω_{i}) \vee Θ_{t \odot s, s} = \cap_{k,r \in w} \big( (Ω_{k} \cap Ω_{r}) \vee Θ_{t \odot s, s} \big) \] for any family of congruences $\{ Ω_{i} : i\in w \}$, with $w$ a possibly infinite set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_00892 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The pairwise distributive law of semilattice congruences Martin-Maroto, Fernando Ricciardo, Antonio de Polavieja, Gonzalo G. Rings and Algebras Commutative Algebra We show that the congruence lattice of a semilattice satsifies a form of distributivity relative to principal congruences of the form $ Θ_{t \odot s, s}$. Particularly, we establish that semilattice congruences obey the ``pairwise distributive law": \[ (\cap_{i \in w} Ω_{i}) \vee Θ_{t \odot s, s} = \cap_{k,r \in w} \big( (Ω_{k} \cap Ω_{r}) \vee Θ_{t \odot s, s} \big) \] for any family of congruences $\{ Ω_{i} : i\in w \}$, with $w$ a possibly infinite set. |
| title | The pairwise distributive law of semilattice congruences |
| topic | Rings and Algebras Commutative Algebra |
| url | https://arxiv.org/abs/2511.00892 |