### Algebra II (Summer Semester 2009)

- Lecturer: PD Dr. Stefan Kühnlein
- Classes: Lecture (1520), Problem class (1521)
- Weekly hours: 4+2

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.

Schedule | ||
---|---|---|

Lecture: | Tuesday 9:45-11:15 | Seminarraum 34 |

Friday 9:45-11:15 | Seminarraum 11 | |

Problem class: | Tuesday 15:45-17:15 | Seminarraum 12 |

Lecturers | ||
---|---|---|

Lecturer | PD Dr. Stefan Kühnlein | |

Office hours: | ||

Room 1.032 Kollegiengebäude Mathematik (20.30) | ||

Email: stefan.kuehnlein@kit.edu | ||

Problem classes | PD Dr. Fabian Januszewski | |

Office hours: jederzeit wenn ich da bin. | ||

Room Kollegiengebäude Mathematik (20.30) | ||

Email: fabian.januszewski@math.uni-paderborn.de |

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.

## Exercises

Problem sheet 3 + Solution to Aufgabe 3

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 12 + Solutions to Aufgabe 2 (c)

# Examination

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

# References

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