A new proof of the Unique Factorization of Z 1 + -d 2 for d = 3, 7, 11, 19, 43, 67, 163
In this paper, we give an elementary proof of the fact that the rings are unique factorization domains for the values d = 3, 7, 11, 19, 43, 67, 163. While the result in itself is well known, our proof is new and completely elementary and uses neither the Minkowski convex body theorem, nor the Dedeki...
- Autores:
-
Ramírez V., Victor J.
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2016
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/66443
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/66443
http://bdigital.unal.edu.co/67471/
- Palabra clave:
- 51 Matemáticas / Mathematics
Unique factorization domain
prime
irreducible
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
| Summary: | In this paper, we give an elementary proof of the fact that the rings are unique factorization domains for the values d = 3, 7, 11, 19, 43, 67, 163. While the result in itself is well known, our proof is new and completely elementary and uses neither the Minkowski convex body theorem, nor the Dedekind and Hasse theorems. Furthermore, it does not use either the theory of algebraic integers, or the theory of Noetherian rings. It only uses basic notions from the theory of commutative rings. |
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