The Macias topology on integral domains
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912092443901952 |
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| author | Macías, Jhixon |
| author_facet | Macías, Jhixon |
| contents | In this manuscript a recent topology on the positive integers generated by the collection of $\{σ_n:n\in\mathbb{N}\}$ where $σ_n:=\{m: \gcd(n,m)=1\}$ is generalized over integral domains. Some of its topological properties are studied. Properties of this topology on infinite principal ideal domains that are not fields are also explored, and a new topological proof of the infinitude of prime elements is obtained (assuming the set of units is finite or not open), different from those presented in the style of H. Furstenberg. Finally, some problems are proposed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_04623 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Macias topology on integral domains Macías, Jhixon General Topology Algebraic Topology In this manuscript a recent topology on the positive integers generated by the collection of $\{σ_n:n\in\mathbb{N}\}$ where $σ_n:=\{m: \gcd(n,m)=1\}$ is generalized over integral domains. Some of its topological properties are studied. Properties of this topology on infinite principal ideal domains that are not fields are also explored, and a new topological proof of the infinitude of prime elements is obtained (assuming the set of units is finite or not open), different from those presented in the style of H. Furstenberg. Finally, some problems are proposed. |
| title | The Macias topology on integral domains |
| topic | General Topology Algebraic Topology |
| url | https://arxiv.org/abs/2406.04623 |