On when the union of two algebraic sets is algebraic
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911944870461440 |
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| author | Aichinger, Erhard Behrisch, Mike Rossi, Bernardo |
| author_facet | Aichinger, Erhard Behrisch, Mike Rossi, Bernardo |
| contents | In universal algebraic geometry, an algebra is called an equational domain if the union of two algebraic sets is algebraic. We characterize equational domains, with respect to polynomial equations, inside congruence permutable varieties, and with respect to term equations, among all algebras of size two and all algebras of size three with a cyclic automorphism. Furthermore, for each size at least three, we prove that, modulo term equivalence, there is a continuum of equational domains of that size. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_00478 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On when the union of two algebraic sets is algebraic Aichinger, Erhard Behrisch, Mike Rossi, Bernardo Rings and Algebras Logic 08A40 (Primary) 08A62, 08B05, 08B10, 20F70 (Secondary) In universal algebraic geometry, an algebra is called an equational domain if the union of two algebraic sets is algebraic. We characterize equational domains, with respect to polynomial equations, inside congruence permutable varieties, and with respect to term equations, among all algebras of size two and all algebras of size three with a cyclic automorphism. Furthermore, for each size at least three, we prove that, modulo term equivalence, there is a continuum of equational domains of that size. |
| title | On when the union of two algebraic sets is algebraic |
| topic | Rings and Algebras Logic 08A40 (Primary) 08A62, 08B05, 08B10, 20F70 (Secondary) |
| url | https://arxiv.org/abs/2309.00478 |