On the direct product of fields with an application
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2019
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| _version_ | 1866912019687407616 |
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| author | Tarizadeh, Abolfazl |
| author_facet | Tarizadeh, Abolfazl |
| contents | In this paper, the (infinite) direct product of fields is investigated. In particular, the finiteness of a given set is characterized in terms of some ring-theoretic observations. Next, a certain localization (whose multiplicative set formed by cofinite sets) of the direct product of fields is studied. Finally, it is shown that every set $X$ can be made into a separated scheme, and this scheme is an affine scheme if and only if $X$ is a finite set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1911_04217 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | On the direct product of fields with an application Tarizadeh, Abolfazl Commutative Algebra Algebraic Geometry 14A05, 14A15, 13A15, 13B30 In this paper, the (infinite) direct product of fields is investigated. In particular, the finiteness of a given set is characterized in terms of some ring-theoretic observations. Next, a certain localization (whose multiplicative set formed by cofinite sets) of the direct product of fields is studied. Finally, it is shown that every set $X$ can be made into a separated scheme, and this scheme is an affine scheme if and only if $X$ is a finite set. |
| title | On the direct product of fields with an application |
| topic | Commutative Algebra Algebraic Geometry 14A05, 14A15, 13A15, 13B30 |
| url | https://arxiv.org/abs/1911.04217 |