by Dilip P Patil (Indian Institute of Science, India) & Uwe Storch (Ruhr University, Germany)

Table of Contents (44k)
Preface (45k)
Chapter 1: Finitely Generated Algebras (185k)

This introductory textbook for a graduate course in pure mathematics provides a gateway into the two difficult fields of algebraic geometry and commutative algebra. Algebraic geometry, supported fundamentally by commutative algebra, is a cornerstone of pure mathematics.

Along the lines developed by Grothendieck, this book delves into the rich interplay between algebraic geometry and commutative algebra. A selection is made from the wealth of material in the discipline, along with concise yet clear definitions and synopses.

• Finitely Generated Algebras
• The K-Spectrum and the Zariski Topology
• Prime Spectra and Dimension
• Schemes
• Projective Schemes
• Regular, Normal and Smooth Points
• Riemann–Roch Theorem