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Algebra II (Summer Semester 2009)

The lectures on Algebra II will be subsequent to Algebra I from Wintersemester 2008/09. However, the dependency will not be very strong, and many topics will be discussed from scratch. The lectures will be given in english as long as this is necessary. The lecture notes will be in german.

There will be a consecutive course on algebraic number theory in Winter 2009/10.

Lecture: Tuesday 9:45-11:15 Seminarraum 34
Friday 9:45-11:15 Seminarraum 11
Problem class: Tuesday 15:45-17:15 Seminarraum 12

During the first 3 or 4 weeks we will learn the universal language of category theory. This is a uniform approach to deal with conceptual questions from any mathematical disciplin.

After this we will discuss several topics from the theory of rings and modules. This will include noetherian modules, tensor products, reducibility, integral ring extensions. In the end I will have to decide whether to treat representation theory of finite groups or Dedekind domains.

On mondays from 15.45 - 17.15 Anja Randecker will give a tutorial in room 1C-04 in the Allianzbau.


Problem sheet 1

Problem sheet 2

Problem sheet 3 + Solution to Aufgabe 3

Problem sheet 4

Problem sheet 5

Problem sheet 6

Problem sheet 7 + Solution to Aufgabe 1 (a) + Solution to Aufgabe 4

Problem sheet 8 Unfortunately, in problem 1 (c) does not imply (a). A counterexample is written up here. Shame on us!

Problem sheet 9 corrected version, there was a small error in the statement of Aufgabe 4.

Problem sheet 10

Problem sheet 11

Problem sheet 12 + Solutions to Aufgabe 2 (c)

Problem sheet 13


There will be oral examinations. Please contact me in order to fix dates.


My Lecture Notes (in german) can be downloaded here (July 28 2009).

Recommended readings are

  • Jacobson: Basic Algebra II
  • Jantzen, Schwermer: Algebra (in german)
  • Lang: Algebra