Perspectives in Mathematical Sciences

The subject for this portion of the course is modules over rings. We show that every (left or right) module over a division ring is free and introduce and classify semi-simple rings. We prove Maschke's theorem that the group ring of a finite group over a field, the characteristic of which does not divide the order of the group, is semi-simple, and study the case of cyclic groups in detail. Finally, we study rings of integers in number fields, where we introduce the ideal class group first considered by Kummer. Here is a more detailed syllabus:

Syllabus in English.

Time and place: Tuesday 2:45-4:15 in Science Building 1, Room 509.

Lecture notes:

Lecture 1: Rings and modules.
Lecture 2: Simple modules.
Lecture 3: Semi-simple rings.
Lecture 4: The discrete Fourier transform.
Lecture 5: The ideal class group.

Report problems:

Report problems. Due Tuesday, May 29, at Science Building 1, Room 105.