Commutative algebra is essentially the study of commutative rings and their modules. It is one of the foundation stones in algebraic geometry and algebraic number theory. For instance, the central notion in commutative algebra is that of prime ideal, which is a common generalization of primes in arithmetic and points in geometry. Roughly speaking, we can also say that commutative algebra provides the local tools for algebraic geometry in the same way as differential analysis provides the tools for differential geometry.
This course is meant to provide a strong foundation in commutative algebra, in order to build the tools to address more advanced topics in commutative algebra, homological algebra, algebraic geometry and algebraic number theory.
- Enseignant: Campanini Federico