On the direct product of fields with an application

Abolfazl Tarizadeh

On the direct product of fields with an application

Commutative Algebra 2024-09-11 v2 Algebraic Geometry

Authors: Abolfazl Tarizadeh

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.

Keywords

direct product of fields cofinite sets localization separated scheme affine scheme ring theory

Cite

@article{arxiv.1911.04217,
  title  = {On the direct product of fields with an application},
  author = {Abolfazl Tarizadeh},
  journal= {arXiv preprint arXiv:1911.04217},
  year   = {2024}
}

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7 pages

On the direct product of fields with an application

Abstract

Keywords

Cite

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