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. We study the case of cyclic groups in detail, where the
description of the group ring afforded by the theorem is known as the
discrete Fourier transform. 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:
Time and place: Tuesday 2:45-4:15 in Science Building 1, Room 509.
Lecture notes:
Report problems: