TU Kaiserslautern • Department of Mathematics • Winter Term 2016/17

«Commutative Algebra»

Prof. Dr. Mathias Schulze • Dipl.-Math. Cornelia Rottner

News

Lecture notes are now available.

Schedule

	weekday	time	room	instructor
class	Tuesday	08:15-09:45	48-438	Mathias Schulze
class	Thursday	08:15-09:45	48-438	Mathias Schulze
tutorial	Wednesday	15:30-17:00	46-268	Cornelia Rottner

Prerequisites

Algebraische Strukturen

Content

rings and ideals, modules, Nakayama's lemma, localization
Noetherian/Artinian rings and modules
primary decomposition
Krull's principal ideal theorem and dimension
integeral extensions, going-up, going-down, normalization
Nother normalization, Hilbert's Nullstellensatz
Dedekind domains, invertible ideals

Homework

There will be weekly homework assignments posted on this page, typically posted on Friday and due on the following Friday by 1:00 pm. Please hand in your solutions by the respective due date in the office of Cornelia Rottner, room 48-427. You may (and you are encouraged to) turn in your homework in teams of 3. However, each of you needs to be able to present your team's solutions during the tutorial.

Problem Set 0 (no due date, to be discussed during the tutorial)
Problem Set 1
Problem Set 2
Problem Set 3
Problem Set 4
Problem Set 5
Problem Set 6
Problem Set 7
Problem Set 8
Problem Set 9
Problem Set 10
Problem Set 11
Problem Set 12

Credit

In order to obtain an Übungsschein you need to actively participate in the tutorial and achieve a total homework score of at least 40%. Active participation includes regular attendance and presenting a solution of a homework problem (at least once). For credit points you need to pass an oral exam after the end of the semester.

Literature

M.F. Atiyah, I.G. Macdonald: Introduction to commutative algebra
H. Matsumura: Commutative Ring Theory
H. Matsumura: Commutative Algebra
D. Eisenbud: Commutative Algebra with a View towards Algebraic Geometry
T. Markwig: Commutative Algebra (lecture notes by Simon Hampe)

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