Commutative Algebra

Contents: Preface. 1. Modules. 2. Localisation. 3. Noetherian rings. 4. Integral extensions. 5. Dedekind domains. 6. Completions. 7. Homology. 8. Dimension. 9. Regular local rings. 10. Some conjectures.

This textbook on commutative algebra presents basic results necessary for elementary algebraic geometry and introduces basic homological algebra and homological methods in commutative algebra. Its lecture-notes style will help readers with some mathematical maturity to study it on their own. Motivations are given at a number of places, examples follow every definition and exercises are given at the end of each section.