Galois Theories of Fields and Rings
This textbook arises from a master’s course taught by the author at the University of Coimbra. It takes the reader from the very classical Galois theorem for fields to its generalization to the case of rings. Given a finite-dimensional Galois extension of fields, the classical bijection between the...
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| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Lenguaje: | inglés |
| Publicado: |
Cham :
Springer Nature Switzerland : Imprint: Springer,
2024.
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| Edición: | 1st ed. 2024. |
| Colección: | Coimbra Mathematical Texts,
2 |
| Materias: | |
| Acceso en línea: | https://doi.org/10.1007/978-3-031-58460-2 |
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Tabla de Contenidos:
- Historical introduction
- Part I Some Galois theorems for fields
- 1 The classical Galois theorem
- 2 The Galois theorem of Grothendieck
- 3 Profinite topological spaces
- 4 The Galois theorems in arbitrary dimension
- Part II The Galois theory of rings
- 5 Adjunctions and monads
- 6 Profinite groupoids and presheaves
- 7 The descent theory of rings
- 8 The Pierce spectrum of a ring
- 9 The Galois theorem for rings
- Further Reading
- Index.