### Algebra II (Summer Semester 2008)

- Lecturer: Prof. Dr. Frank Herrlich
- Classes: Lecture (1520), Problem class (1521)
- Weekly hours: 4+2
- Audience: Mathematics (including International Master), Computer Science

In this course we treat part of what usually is called **Commutative Algebra**.

The key notion is that of a **module over a ring**. It generalizes the familiar vector spaces over a field to the situation where the coefficients live in a more general ring.

The course is part of the International Master Program in Mathematics and will be held **in english**.

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

Lecture: | Wednesday 9:45-11:15 | Seminarraum 12 |

Friday 9:45-11:15 | Seminarraum 12 | |

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

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

Lecturer | Prof. Dr. Frank Herrlich | |

Office hours: By appointment (per e-mail) | ||

Room 1.022 Kollegiengebäude Mathematik (20.30) | ||

Email: herrlich@kit.edu | ||

Problem classes | Ute Luhm | |

Office hours: freitags, 10.00-12.00 Uhr, Zimmer 4A-21.2 (auf der Brücke) | ||

Room Allianz-Gebäude (05.20) | ||

Email: |

In the first part we deal with multilinear algebra for modules over a ring.

This includes construction and properties of the tensor product and the exterior product of modules, the study of derivatives and differentials from an algebraic point of view, and also the beginnings of homological algebra.

The second part is concerned with properties and structure theorems for noetherian rings. Highlights are Hilbert's Nullstellensatz, the theorems of Cohen-Seidenberg on integral ring extensions as well as the characterization of discrete valuation rings and Dedekind domains.

This course is a good basis for advanced courses and seminars in Number Theory and Algebraic Geometry.

For the winter term 2008/09 we plan a course on Algebraic Geometry.

# Exercises

Problem sessions start on Tuesday, 22.4.2008.

There will be a problem sheet once a week. You can solve the exercises in pairs.

# Examination

At the end of the summer term we offer oral examinations.