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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.
Sample Chapter(s)
Chapter 1: Finitely Generated Algebras (185 KB)
Contents:
- 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
Readership: Students and professionals in mathematics.
