Towards an Enumeration of Finite Common Meadows
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911909684445184 |
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| author | Dias, João Dinis, Bruno |
| author_facet | Dias, João Dinis, Bruno |
| contents | Common meadows are commutative and associative algebraic structures with two operations (addition and multiplication) with additive and multiplicative identities and for which inverses are total. The inverse of zero is an error term $\mathbf{a}$ which is absorbent for addition. We study the problem of enumerating all finite common meadows of \emph{order} $n$ (that is, common meadows with $n$ elements). This problem turns out to be deeply connected with both the number of finite rings of order $n$ and with the number of a certain kind of partition of positive integers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_10631 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Towards an Enumeration of Finite Common Meadows Dias, João Dinis, Bruno Rings and Algebras Common meadows are commutative and associative algebraic structures with two operations (addition and multiplication) with additive and multiplicative identities and for which inverses are total. The inverse of zero is an error term $\mathbf{a}$ which is absorbent for addition. We study the problem of enumerating all finite common meadows of \emph{order} $n$ (that is, common meadows with $n$ elements). This problem turns out to be deeply connected with both the number of finite rings of order $n$ and with the number of a certain kind of partition of positive integers. |
| title | Towards an Enumeration of Finite Common Meadows |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2401.10631 |