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A course in commutative algebra / Gregor Kemper.

By: Kemper, Gregor, 1963-.
Material type: TextTextSeries: Graduate texts in mathematics: 256.Publisher: Dordrecht ; New York : Springer, c2011Description: xi, 246 p., E 24.99 ill. ; 25 cm.ISBN: 9783642035449 (hbk. : alk. paper); 3642035442 (hbk. : alk. paper); 9783642035456 (eISBN).Subject(s): Commutative algebra | Algebra | Mathematics | Algebra commutativa | Matematica | Kommutative AlgebraDDC classification: 512.4/4 Other classification: 510 Online resources: Inhaltsverzeichnis
Contents:
Introduction ---- Part I. The Algebra-Geometry Lexicon. 1. Hilberts 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.--
Item type Current location Call number Status Date due Barcode Item holds
Book Chennai Mathematical Institute
General Stacks 		512.44 KEM (Browse shelf) Checked out 01/05/2024 9116
Total holds: 0

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

Introduction ---- Part I. The Algebra-Geometry Lexicon. 1. Hilberts 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.--