A Course in Commutative Algebra

✍ Scribed by Gregor Kemper (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2011
• Tongue: English
• Leaves: 259
• Series: Graduate Texts in Mathematics 256
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xi
Introduction....Pages 1-4
Front Matter....Pages 5-5
Hilbert’s Nullstellensatz....Pages 7-21
Noetherian and Artinian Rings....Pages 23-32
The Zariski Topology....Pages 33-44
A Summary of the Lexicon....Pages 45-48
Front Matter....Pages 49-49
Krull Dimension and Transcendence Degree....Pages 51-61
Localization....Pages 63-73
The Principal Ideal Theorem....Pages 75-91
Integral Extensions....Pages 93-114
Front Matter....Pages 115-115
Gröbner Bases....Pages 117-136
Fibers and Images of Morphisms Revisited....Pages 137-150
Hilbert Series and Dimension....Pages 151-164
Front Matter....Pages 165-165
Dimension Theory....Pages 167-179
Regular Local Rings....Pages 181-196
Rings of Dimension One....Pages 197-216
Back Matter....Pages 217-246

✦ Subjects

Algebraic Geometry; Commutative Rings and Algebras; Computational Mathematics and Numerical Analysis