Course in commutative algebra
by Kemper, Gregor.Material type: BookSeries: 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
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Central Library, IISER Bhopal
OPAC URL: http://webopac.iiserb.ac.in/
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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 M314I Introduction to the theory of schemes||516.35 M919A Algebraic Geometry I :||516.35 P79R Rational points on varieties|
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.--