A Sheaf Model of the Algebraic Closure

Bassel Mannaa, Thierry Coquand

Research output: Journal Article or Conference Article in JournalJournal articleResearchpeer-review

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.
Original languageUndefined/Unknown
JournalEPTCS
ISSN2075-2180
DOIs
Publication statusPublished - 17 Apr 2014
Externally publishedYes

Cite this