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Course in commutative algebra Gregor Kemper.

By: Series: Graduate texts in mathematics ; 256.Publication details: New York : Springer, c2011.Description: xi, 246 p. : ill. ; 25 cmISBN:
  • 9783642035449 (Hbk)
Subject(s): DDC classification:
  • 516.35 K32C 23
LOC classification:
  • QA251.3 .K456 2011
Online resources:
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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Item type Current library Collection Call number Status Notes Date due Barcode
Books Books Central Library, IISER Bhopal Reference Section Reference 516.35 K32C (Browse shelf(Opens below)) Not For Loan Reserve 8384

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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