抽象代数讲义（第3卷）（英文） [Lectures in Abstract Algebra 3] epub pdf mobi txt 电子书 下载 2024

抽象代数讲义（第3卷）（英文） [Lectures in Abstract Algebra 3] epub pdf mobi txt 电子书 下载 2024

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抽象代数讲义（第3卷）（英文） [Lectures in Abstract Algebra 3] epub pdf mobi txt 电子书 下载 2024

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内容简介

　　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.

内页插图

目录

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

前言/序言

抽象代数讲义（第3卷）（英文） [Lectures in Abstract Algebra 3] epub pdf mobi txt 电子书 下载 2024

抽象代数讲义（第3卷）（英文） [Lectures in Abstract Algebra 3] 下载 epub mobi pdf txt 电子书 2024

评分☆☆☆☆☆

一块买了几本书，结果每本书品相都不怎么样，是不是觉得买的多，给你差一点的也无所谓。

评分☆☆☆☆☆

不错不错不错不错不错不错不错不错

评分☆☆☆☆☆

好书啊，要认真学习一下了

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好

评分☆☆☆☆☆

学抽象代数很不错的一本书

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很便宜，书很好

评分☆☆☆☆☆

读着可能枯燥，但是读进去会有收益

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英文原版，原汁原味。

评分☆☆☆☆☆

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.

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