Varieties defined by linear equations have the amalgamation property
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866917759849332736 |
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| author | Lipparini, Paolo |
| author_facet | Lipparini, Paolo |
| contents | A variety is a class of algebraic structures axiomatized by a set of equations. An equation is linear if there is at most one occurrence of an operation symbol on each side. We show that a variety axiomatized by linear equations has the strong amalgamation property.
Suppose further that the language has no constant symbol and, for each equation, either one side is operation-free, or exactly the same variables appear on both sides. Then also the joint embedding property holds.
Examples include most varieties defining classical Maltsev conditions. In a few special cases, the above properties are preserved when further unary operations appear in the equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_14316 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Varieties defined by linear equations have the amalgamation property Lipparini, Paolo Logic Rings and Algebras 03C05, 03C52, 08B05, 08B25 A variety is a class of algebraic structures axiomatized by a set of equations. An equation is linear if there is at most one occurrence of an operation symbol on each side. We show that a variety axiomatized by linear equations has the strong amalgamation property. Suppose further that the language has no constant symbol and, for each equation, either one side is operation-free, or exactly the same variables appear on both sides. Then also the joint embedding property holds. Examples include most varieties defining classical Maltsev conditions. In a few special cases, the above properties are preserved when further unary operations appear in the equations. |
| title | Varieties defined by linear equations have the amalgamation property |
| topic | Logic Rings and Algebras 03C05, 03C52, 08B05, 08B25 |
| url | https://arxiv.org/abs/2105.14316 |