Infinite Atomized Semilattices
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917098923491328 |
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| author | Martin-Maroto, Fernando Ricciardo, Antonio Mendez, David de Polavieja, Gonzalo G. |
| author_facet | Martin-Maroto, Fernando Ricciardo, Antonio Mendez, David de Polavieja, Gonzalo G. |
| contents | We extend the theory of atomized semilattices to the infinite setting. We show that it is well-defined and that every semilattice is atomizable. We also study atom redundancy, focusing on complete and finitely generated semilattices and show that for finitely generated semilattices, atomizations consisting exclusively of non-redundant atoms always exist. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_01389 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Infinite Atomized Semilattices Martin-Maroto, Fernando Ricciardo, Antonio Mendez, David de Polavieja, Gonzalo G. Commutative Algebra Rings and Algebras 06A12, 08B26, 08B20 We extend the theory of atomized semilattices to the infinite setting. We show that it is well-defined and that every semilattice is atomizable. We also study atom redundancy, focusing on complete and finitely generated semilattices and show that for finitely generated semilattices, atomizations consisting exclusively of non-redundant atoms always exist. |
| title | Infinite Atomized Semilattices |
| topic | Commutative Algebra Rings and Algebras 06A12, 08B26, 08B20 |
| url | https://arxiv.org/abs/2311.01389 |