A course in commutative algebra
著者
書誌事項
A course in commutative algebra
（Graduate texts in mathematics, 256）
Springer, c2011
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注記
Includes bibliographical references (p. 235-237) and index
内容説明・目次
内容説明
This textbook offers a thorough, modern introduction into commutative algebra. It is intented mainly to serve as a guide for a course of one or two semesters, or for self-study. The carefully selected subject matter concentrates on the concepts and results at the center of the field. The book maintains a constant view on the natural geometric context, enabling the reader to gain a deeper understanding of the material. Although it emphasizes theory, three chapters are devoted to computational aspects. Many illustrative examples and exercises enrich the text.
目次
- Introduction.- Part I The Algebra Geometry Lexicon: 1 Hilbert's Nullstellensatz
- 2 Noetherian and Artinian Rings
- 3 The Zariski Topology
- 4 A Summary of the Lexicon.- Part II Dimension: 5 Krull Dimension and Transcendence Degree
- 6 Localization
- 7 The Principal Ideal Theorem
- 8 Integral Extensions.- Part III Computational Methods: 9 Groebner Bases
- 10 Fibers and Images of Morphisms Revisited
- 11 Hilbert Series and Dimension.- Part IV Local Rings: 12 Dimension Theory
- 13 Regular Local Rings
- 14 Rings of Dimension One.- References.- Notation.- Index.
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