抽象代數講義（第3捲）（英文） [Lectures in Abstract Algebra 3] epub pdf mobi txt 電子書 下載 2025

抽象代數講義（第3捲）（英文） [Lectures in Abstract Algebra 3] epub pdf mobi txt 電子書 下載 2025

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抽象代數講義（第3捲）（英文） [Lectures in Abstract Algebra 3] epub pdf mobi txt 電子書 下載 2025

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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.

內頁插圖

目錄

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

抽象代數講義（第3捲）（英文） [Lectures in Abstract Algebra 3] epub pdf mobi txt 電子書 下載 2025

抽象代數講義（第3捲）（英文） [Lectures in Abstract Algebra 3] 下載 epub mobi pdf txt 電子書

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一塊買瞭幾本書，結果每本書品相都不怎麼樣，是不是覺得買的多，給你差一點的也無所謂。

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經典圖書，值得擁有！！！

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讀著可能枯燥，但是讀進去會有收益

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書很好 很滿意 下次還買

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學抽象代數很不錯的一本書

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好好好好好好

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好書啊，要認真學習一下瞭

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英文原版，原汁原味。

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