Thomas Markwig Reading Course Commutative Algebra - ST 2011
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Dates:

Meeting: Fr 13:45-15:15, Rm 48-436

News:

  • The course is based on the notes which Simon Hampe took throughout one of my courses. A part of chapter 1 you will find in my own notes. Please let me know if you find any errors or misprints.

  • Plan
    Week 1 1.1-1.9
    Week 2 1.10-1.18
    Week 3 1.19-1.44
    Week 4 2.1-2.25
    Week 5 2.26-2.40
    Week 6 3.1-3.18
    Week 7 3.19-4.24
    Week 8 5.1-5.22
    Week 9 5.23-6.8
    Week 10 6.9-7.1
    Week 11 7.2-7.14
    Week 12 7.15-8.4
    Week 13 8.5-8.22
    Week 14 8.23-8.35

  • There will be no meetings on Friday, 22nd April, 17th June, and 8th July. Instead the meeting on the following Friday will last longer to discuss the contents of the two weeks.

Assingments / Notes:

PDF Dateien: Lecture Notes , Transparencies , 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 .

Literature:

Michael F. Atiyah, Ian G. MacDonald Introduction to Commutative Algebra, Addison Wesley.
Hideyuki Matsumura, Commutative Ring Theory, CUP.
Hideyuki Matsumura, Commutative Algebra.
David Eisenbud, Commutative Algebra with a View towards Algebraic Geometry, Springer.
Gert-Martin Greuel, Gerhard Pfister, A Singular Introduction to Commutative Algebra, Springer.
Winfried Bruns, Zahlentheorie, Osnabrücker Schriften zur Mathematik.

Content:

Rings and ideals, modules, Nakayama lemma, localization, Noetherian and Artinian rings, primary decomposition, Noether normalization and applications (finite and integral extensions, integral closure, dimension, Hilbert's Nullstellensatz), Krull's Principle Ideal Theorem, Dedekind domains.

Univ. of TübingenDept. of MathematicsSection AlgebraCAS SINGULAR