The p-adic integers as a quotient of a ring of power series
Let p a prime number. The most familiar construction of the ring of p-adic integers ℤp, is as the projective limit of quotients of powers of the ideal (p)◁ℤ. There is another description of ℤp as a quotient of the power series ring ℤ[[X]], which can be found in some texts of p-adic analysis (see e.g...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2022 |
| País: | Perú |
| Institución: | Universidad Nacional Mayor de San Marcos |
| Repositorio: | Revistas - Universidad Nacional Mayor de San Marcos |
| Idioma: | español |
| OAI Identifier: | oai:revistasinvestigacion.unmsm.edu.pe:article/21522 |
| Acceso en línea: | https://revistasinvestigacion.unmsm.edu.pe/index.php/matema/article/view/21522 |
| Access Level: | acceso abierto |
| Palabra clave: | p-adic Integers Power Seies Projective Limit isomorphism quotient Enteros p-ádicos Series de Potencias Límite Proyectivo isomorfismo cociente |
| Sumario: | Let p a prime number. The most familiar construction of the ring of p-adic integers ℤp, is as the projective limit of quotients of powers of the ideal (p)◁ℤ. There is another description of ℤp as a quotient of the power series ring ℤ[[X]], which can be found in some texts of p-adic analysis (see e.g. [3]). More specifically, there exists a ring isomorphism. Ψ : ℤ[[X]]/〈p − X〉 → ℤp. However, this isomorphism is also topological in nature, but there is no proof of this fact in the corresponding literature. In this article we will prove in sufficient detail that the above description is also valid in the context of topological rings. |
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