Advanced Modern Algebra

基本信息

Series:Graduate Studies in Mathematics

Format:Hardback 1264 pages

Publisher:American Mathematical Society

Imprint:American Mathematical Society

ISBN:9781470441746

Published:30 Aug 2017

Classifications:Algebra, Algebraic geometry

Readership:Professional & Vocational

Weight:2530g

Dimensions:204 x 277 x 73 (mm)

页面参数仅供参考，具体以实物为准

书籍简介

新版《高等近世代数 第3版》分为两部分，已经进行了重大的重组，许多部分已经重写。第一部分是为第一年的研究生代数设计的，包括两门课程:伽罗瓦理论和模块理论。第一节课涉及的是三次和四次方程解的经典公式、经典数论、交换代数、群和伽罗瓦理论。

第二门课程的主题是Zorn的理、标准形式、内积空间、范畴和极限、张量积、射影、离散和平坦模、多重线性代数、仿射变换和格罗伯纳基。第二部分将更深入、更详细地介绍第一部分中提到的许多主题。该书共分五章，分别介绍了群论、表示论、同调代数、范畴和交换代数。

本书可以作为第二门抽象代数研究生课程的教材，也可以作为第一门抽象代数研究生课程的补充材料，或者用作自学。

This new edition, now in two parts, has been significantly reorganized and many sections have been rewritten. The first part, designed for a first year of graduate algebra, consists of two courses: Galois theory and Module theory. Topics covered in the first course are classical formulas for solutions of cubic and quartic equations, classical number theory, commutative algebra, groups, and Galois theory.

Topics in the second course are Zorn's lemma, canonical forms, inner product spaces, categories and limits, tensor products, projective, injective, and flat modules, multilinear algebra, affine varieties, and Grobner bases. The second part presents many topics mentioned in the first part in greater depth and in more detail. The five chapters of the book are devoted to group theory, representation theory, homological algebra, categories, and commutative algebra, respectively.

The book can be used as a text for a second abstract algebra graduate course, as a source of additional material to a first abstract algebra graduate course, or for self-study.

目录

Contents for Part 1:

Course I: Classical formulas

Classical number theory

Commutative rings

Groups

Galois theory

Appendix: Set theory

Appendix: Linear algebra

Course II: Modules

Zorn's lemma

Advanced linear algebra

Categories of modules

Multilinear algebra

Commutative algebra II

Appendix: Categorical limits

Appendix: Topological spaces

Bibliography

Special notation

Index

Contents for Part 2: More groups

Representation theory

Homology

More categories

Commutative rings III

Bibliography

Index.

作者简介

Joseph J．Rotman美国伊利诺伊大学厄巴纳-尚佩恩分校数学系教授。他著有多部数学方面的书，其中包括《A First Course in Abstract Algebra》(抽象代数基础教程，本书影印版、中文版由机械工业出版社引进出版)、《Galois Theory》等。

Joseph J. Rotman, University of Illinois at Urbana-Champaign, IL.