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Course in commutative algebra

by Kemper, Gregor.
Material type: materialTypeLabelBookSeries: Graduate texts in mathematics: 256.Publisher: New York : Springer, c2011Description: xi, 246 p. : ill. ; 25 cm.ISBN: 9783642035449 (Hbk).Subject(s): Commutative algebra | Algebra | Mathematics | Àlgebra commutativa | Matemàtica | Kommutative AlgebraDDC classification: 516.35 K32C Online resources: Inhaltsverzeichnis
Contents:
Introduction ---- Part I. The Algebra-Geometry Lexicon. 1. Hilbertʹs 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. Grobner 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 ---- Solutions of Some Exercises.
Summary: 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.--
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Reference Section 		Reference 516.35 K32C (Browse shelf) Not For Loan Reserve 8384
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516.35 H98F Fourier-Mukai transforms in algebraic geometry 516.35 J26M Motives 516.35 J26M Motives 516.35 K32C Course in commutative algebra 516.35 M22I Introduction to tropical geometry 516.35 M314I Introduction to the theory of schemes 516.35 M919A Algebraic Geometry I :

Includes bibliographical references (p. 235-237) and indexes.

Introduction ---- Part I. The Algebra-Geometry Lexicon. 1. Hilbertʹs 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. Grobner 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 ---- Solutions of Some Exercises.

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.--

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