Mathematics 251: Basic Graduate Algebra (Fall 2003)
Instructor
Chad Schoen
Description
This is a basic graduate level introduction to algebra. The topics
are rings, modules, fields and field extensions. Group theory will
receive scant attention, only a brief review of what is necessary
for Galois theory aimed at students with previous exposure to the
subject will be included.
Topics include: Rings, ideals, unique factorization domains. Modules,
finitely generated modules over principal ideal domains and applications.
Algebraic field extensions, separable and inseparable extensions,
finite fields, Galois theory, Kummer theory, solvability by radicals.
We will follow the final five chapters in the book, Algebra, by Michael
Artin with various deletions and additions.
Further topics as time permits.
Prerequisites
Most students
who take math 251 will have had a one or two semester undergraduate
algebra course. Such a background will certainly be helpful, although
perhaps not essential, since rings and modules will be covered
(rapidly) from scratch. On the other hand some knowledge of group
theory will be assumed.
Text
- Algebra, by Michael Artin.
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