A Sheaf Model of the Algebraic Closure
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 characterist...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Open Publishing Association
2014-09-01
|
| Series: | Electronic Proceedings in Theoretical Computer Science |
| Online Access: | http://arxiv.org/pdf/1404.4549v4 |
| Summary: | 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. |
|---|---|
| ISSN: | 2075-2180 |