Commutative Algebra: with a View Toward Algebraic Geometry
Commutative Algebra: with a View Toward Algebraic Geometry
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DOI：
10.1007/978-1-4612-5350-1
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发表时间：
1995-03
期刊：
影响因子：
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通讯作者：
D. Eisenbud
中科院分区：
文献类型：
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作者：
D. Eisenbud
对交换代数的最好理解是对几何思想的了解，这些思想在交换代数的形成中发挥了重要作用，简而言之，就是对代数几何的看法。作者从交换代数的基本概念，如局部化和初等分解，到维数论、微分、同调方法、自由分辨和对偶，对交换代数进行了全面的介绍，强调了交换代数思想的起源及其与数学其他部分的联系。许多练习说明和锐化理论和扩展练习给读者一个积极的部分，以补充在文本中提出的材料。一个新颖的特点是一章致力于快速而彻底地处理Grobner基理论和交换代数和代数几何中由此产生的构造方法。文中还包括了该理论的应用，以及对计算机代数项目的建议。这本书将吸引读者从初学者到交换代数或代数几何的高级学生。为了帮助初学者，从代数几何的基本理想从头开始处理。关于同态代数的附录，多线性代数和其他一些有用的主题有助于使这本书相对独立。新颖的结果和演示分散在整个文本中。
Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry. The author presents a comprehensive view of commutative algebra, from basics, such as localization and primary decomposition, through dimension theory, differentials, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. Many exercises illustrate and sharpen the theory and extended exercises give the reader an active part in complementing the material presented in the text. One novel feature is a chapter devoted to a quick but thorough treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Applications of the theory and even suggestions for computer algebra projects are included. This book will appeal to readers from beginners to advanced students of commutative algebra or algebraic geometry. To help beginners, the essential ideals from algebraic geometry are treated from scratch. Appendices on homological algebra, multilinear algebra and several other useful topics help to make the book relatively self-contained. Novel results and presentations are scattered throughout the text.