Abstract Algebra Suitable for Self-Study or Online Lectures /
This book contains the fundamental basics of algebra at university level. In addition to elementary algebraic structures such as groups, rings and fields, the text in particular covers Galois theory together with its applications to cyclotomic fields, finite fields as well as solving polynomial equa...
I tiakina i:
| Kaituhi matua: | |
|---|---|
| Kaituhi rangatōpū: | |
| Hōputu: | Tāhiko īPukapuka |
| Reo: | Ingarihi |
| I whakaputaina: |
Berlin, Heidelberg :
Springer Berlin Heidelberg : Imprint: Springer,
2024.
|
| Putanga: | 1st ed. 2024. |
| Rangatū: | Mathematics Study Resources,
7 |
| Ngā marau: | |
| Urunga tuihono: | https://doi.org/10.1007/978-3-662-67974-6 |
| Ngā Tūtohu: |
Tāpirihia he Tūtohu
Kāore He Tūtohu, Me noho koe te mea tuatahi ki te tūtohu i tēnei pūkete!
|
Rārangi ihirangi:
- Motivation and prerequisites
- Field extensions and algebraic elements
- Groups
- Group quotients and normal divisors
- Rings and ideals
- Euclidean rings, principal ideal rings, Noetherian rings
- Factorial rings
- Quotient fields for integrality domains
- Irreducible polynomials in factorial rings
- Galois theory (I) - Theorem A and its variant A'
- Intermezzo - explicit example
- Normal fields extensions
- Separability
- Galois theory (II) - The main theorem
- Cyclotomic fields
- Finite fields
- More group theory - Group operations and Sylow
- Resolvability of polynomial equations.