A Course in Commutative Algebra

Authors:

ISBN: 978-3-642-03544-9 (Print) 978-3-642-03545-6 (Online)

Table of contents (15 chapters)

  1. Front Matter

    Pages i-xi

  2. No Access

    Book Chapter

    Pages 1-4

    Introduction

  3. The Algebra–Geometry Lexicon

    1. Front Matter

      Pages 5-5

    2. No Access

      Book Chapter

      Pages 7-21

      Hilbert’s Nullstellensatz

    3. No Access

      Book Chapter

      Pages 23-32

      Noetherian and Artinian Rings

    4. No Access

      Book Chapter

      Pages 33-44

      The Zariski Topology

    5. No Access

      Book Chapter

      Pages 45-48

      A Summary of the Lexicon

  4. Dimension

    1. Front Matter

      Pages 49-49

    2. No Access

      Book Chapter

      Pages 51-61

      Krull Dimension and Transcendence Degree

    3. No Access

      Book Chapter

      Pages 63-73

      Localization

    4. No Access

      Book Chapter

      Pages 75-91

      The Principal Ideal Theorem

    5. No Access

      Book Chapter

      Pages 93-114

      Integral Extensions

  5. Computational Methods

    1. Front Matter

      Pages 115-115

    2. No Access

      Book Chapter

      Pages 117-136

      Gröbner Bases

    3. No Access

      Book Chapter

      Pages 137-150

      Fibers and Images of Morphisms Revisited

    4. No Access

      Book Chapter

      Pages 151-164

      Hilbert Series and Dimension

  6. Local Rings

    1. Front Matter

      Pages 165-165

    2. No Access

      Book Chapter

      Pages 167-179

      Dimension Theory

    3. No Access

      Book Chapter

      Pages 181-196

      Regular Local Rings

    4. No Access

      Book Chapter

      Pages 197-216

      Rings of Dimension One

  7. Back Matter

    Pages 217-246