COMMUTATIVE ALGEBRA
cod. 1000143

Learning objectives

The students will learn the basic definitions, problems, and techniques in Commutative Algebra. At the end of the course, they will be able to solve basic exercises in the context of commutative ring theory.

Prerequisites

Algebra.

Course unit content

The course is an introduction to Commutative Algebra with a focus on the interplay between Algebra and Geometry in the theory of commutative rings.

Full programme

Basic notions: rings, ideals, modules. Noetherian and Artinian rings. Dedekind domains. Dimension theory. Homological algebra.

Bibliography

[AMD] M.F. Atiyah, I.G. MacDonald, Introduction to Commutative Algebra
[E] D. Eisenbud, Commutative Algebra with a view towards Algebraic Geometry
[AK] Altman, Kleiman, A term in Commutative Algebra

Teaching methods

The topics of the course will be discussed during the online lectures, together with examples, applications, and exercises.

Assessment methods and criteria

Every forth-night one lecture will be focused on exercises, both computational and theoretical. At the end of the course there will be a written exam. A passing grade will give access to a subsequent oral exam, consisting in an interview at the board, during which the student will be asked to discuss, explain, and prove the main results of the course.

Other information