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arXiv · 1911.04217

On the direct product of fields with an application

Abolfazl Tarizadeh
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Abstract

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.

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Abolfazl Tarizadeh. 2019-11-11. On the direct product of fields with an application. https://arxiv.org/abs/1911.04217

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