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Abstract
This course provides an introduction to commutative algebra. It serves in particular as a foundation for modern algebraic geometry.
Objective
The topics presented in the course will include: * Basics facts about rings, ideals and modules * Constructions of rings: quotients, polynomial rings, localization * Noetherian rings and modules * The tensor product of modules over commutative rings and its applications * Krull dimension * Integral extensions and the Cohen-Seidenberg theorems * Finitely generated algebrais over fields, including the Noether Normalization Theorem and the Nullstellensatz * Primary decomposition * Discrete valuation rings and some applications
Resources
Literature
Primary Reference: "(Mostly) Commutative Algebra", by A. Chambert-Loir; Springer 2021, available on the author's web page. Secondary References: 1. "Introduction to Commutative Algebra" by M. F. Atiyah and I. G. Macdonald (Addison-Wesley Publ., 1969) 2. "Commutative algebra. With a view towards algebraic geometry" by D. Eisenbud (GTM 150, Springer Verlag, 1995) 3. "Commutative ring theory" by H. Matsumura (Cambridge University Press 1989) 4. "Commutative Algebra" by N. Bourbaki
General Information
- Language
- English
- Levels
- BSC , MSC
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- oral 30 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture |
Commutative Algebra
Does not take place this semester.
|
No time listed | 4 h weekly |
| exercise |
Commutative Algebra
Does not take place this semester.
|
No time listed | 1 h weekly |
Offered In
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Core Courses (For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 15 of the required 28 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.)
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