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抽象代數講義-第3卷 版權信息
- ISBN:9787510061530
- 條形碼:9787510061530 ; 978-7-5100-6153-0
- 裝幀:一般膠版紙
- 冊數:暫無
- 重量:暫無
- 所屬分類:>>
抽象代數講義-第3卷 本書特色
《抽象代數講義》是一套久負盛名的三卷集教材,是作者雅格布斯根據他在霍普金斯大學和耶魯大學講課時的講義編寫而成的,后又成為作者《基本代數學》一書的藍本。《抽象代數講義(第3卷)》介紹域理論和伽羅瓦理論,討論了域的代數結構和域的賦值理論。本書為全英文版本。
抽象代數講義-第3卷 內容簡介
The present Vrolume completes the series of texts on algebra which the author began more than ten years ago. The account of field theory and Galois theory which we girre here is based on the notions and results of general algebra which appear in our first volume and on the more elementary parts of the second volume, dealing with linear algebra. The level of the present work .is roughly the same as that of Volume II.
抽象代數講義-第3卷 目錄
S ECTION
1. Extension of homomorphisms
2. Algebras
3. Tensor products of vector spaces
4. Tensor product of algebras
CHAPTER I: FINITE DIMENSIONAL EXTENSION FIELDS
1 Some vector spaces associated with mappings of fields
2. The Jacobson-Bourbaki correspondence
3. Dedekind independence theorem for isomorphisms of a field
4. Finite groups of automorphisms.
5. Splitting field of a polynomial
6. Multiple roots. Separable polynomials
7. The "fundamental theorem" of Galois theory INTRODUCTION
S ECTION
1. Extension of homomorphisms
2. Algebras
3. Tensor products of vector spaces
4. Tensor product of algebras
CHAPTER I: FINITE DIMENSIONAL EXTENSION FIELDS
1 Some vector spaces associated with mappings of fields
2. The Jacobson-Bourbaki correspondence
3. Dedekind independence theorem for isomorphisms of a field
4. Finite groups of automorphisms.
5. Splitting field of a polynomial
6. Multiple roots. Separable polynomials
7. The "fundamental theorem" of Galois theory
8. Normal extensions. Normal closures
9. Structure of algebraic extensions. Separability
10. Degrees of separability and inseparability. Structure of normal extensions
11. Primitive elements
12. Normalbases
13. Finitefields
14. Regular representation, trace and norm
15. Galois cohomology
16. Composites of fields
CHAPTER II: GALOIS THEORY OF EQUATIOIVS
1. The Galois group of an equation
2. Pureequations
3. Galois' criterion for solvability by radicals
4. The general equation of n-th degree
5. Equations with rational coefficients and symmetric group as Galoisgroup
CHAPTER Ⅲ: ABELIAN EXTENSlONS
1. Cyclotomic fields over the rationals
2. Characters of finite commutatiye groups
3. Kummer extensions
4. Witt rrectors
5. Abelian p-extensions
CHAPTER Ⅳ: STRUCTURE THEORY OF FIELDS
1 Algebraically closed fields
2. Infinite Galois theory
3. Transcendency basis
4. Luroth's theorem.
5. Linear disjointness and separating transcendency bases
6. Derivations
7. Derivations, separability and p-independence
8. Galois theory for purely inseparable extensions of exponert one
9. Higher derivations
10. Tensor products of fields
11. Free composites offields
CHAPTER V: VALUATION .THEORY
1. Realvaluations
2. Real valuations of the field of rational numbers
3. Real valuations of (x) which are trivial in
4. Completionofafield
5. Some properties of the field of p-adic numbers
6. Hensel'slemma
7. Construction of complete fields with given residue fields
8. Ordered groups and-valuations
9. Valuations, valuation rings, and places
10. Characterization of real non-archimedean valuations
11. Extension of homomorphisms and valuations
12. Application of the extension theorem: Hilbert Nullstellensatz
13. Application of the extension theorem: integral closure
……
CHAPTER VI: ARTIN-SCHREIER THEORY
Index
抽象代數講義-第3卷 節選
《抽象代數講義》是一套久負盛名的三卷集教材,是作者雅格布斯根據他在霍普金斯大學和耶魯大學講課時的講義編寫而成的,后又成為作者《基本代數學》一書的藍本。《抽象代數講義(第3卷)》介紹域理論和伽羅瓦理論,討論了域的代數結構和域的賦值理論。本書為全英文版本。
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¥36.3¥44.1