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arXiv · 1404.4549

A Sheaf Model of the Algebraic Closure

Bassel Mannaa·Thierry Coquand
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Abstract

In constructive algebra one cannot in general decide the irreducibility of a polynomial over a field K. This poses some problems to showing the existence of the algebraic closure of K. We give a possible constructive interpretation of the existence of the algebraic closure of a field in characteristic 0 by building, in a constructive metatheory, a suitable site model where there is such an algebraic closure. One can then extract computational content from this model. We give examples of computation based on this model.

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BibTeXRIS

Bassel Mannaa, Thierry Coquand. 2014-09-11. A Sheaf Model of the Algebraic Closure. https://doi.org/10.4204/eptcs.164.2

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