Arithmetic and $k$-maximality of the cyclic free magma
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909267310673920 |
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| author | Cardó, Carles |
| author_facet | Cardó, Carles |
| contents | We survey free magmas and we explore the structure of their submagmas. By equipping the cyclic free magma with a second distributive operation we obtain a ringoid-like structure with some primitive arithmetical properties. A submagma is $k$-maximal when there are only $k-1$ submagmas between it and the free magma itself. These two tools, arithmetic and maximality, allow us to study the lattice of the submagmas of a free magma. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_17692 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Arithmetic and $k$-maximality of the cyclic free magma Cardó, Carles Rings and Algebras 08A02, 08B20, 20N99, 03G10 We survey free magmas and we explore the structure of their submagmas. By equipping the cyclic free magma with a second distributive operation we obtain a ringoid-like structure with some primitive arithmetical properties. A submagma is $k$-maximal when there are only $k-1$ submagmas between it and the free magma itself. These two tools, arithmetic and maximality, allow us to study the lattice of the submagmas of a free magma. |
| title | Arithmetic and $k$-maximality of the cyclic free magma |
| topic | Rings and Algebras 08A02, 08B20, 20N99, 03G10 |
| url | https://arxiv.org/abs/2407.17692 |