Cornell Math - MATH 631, Fall 2000

MATH 631 — Fall 2000
Algebra

Math 631 is the introductory graduate algebra course. A prerequisite for it is an undergradate modern algebra course such as Math 434. Also a knowledge of linear algebra at the level of Math 433 will be assumed, though not much direct use will be made of it. The material falls naturally into three parts with, however, many interconnections. A partial list of topics follows:

Group Theory: Subgroups, normal subgroups, quotient groups, group actions, Sylow theorems, composition series.

Rings and Modules: Subrings, ideals, quotient rings, principal ideal domains, modules, fundamental theorem on finitely generated modules over a PID, application to abelian groups, tensor products.

Fields: Field extensions, Galois theory, application to the theory of equations (solvability by radicals etc.).

Note that there is a considerable overlap with Math 434 but that the pace will be much faster during the "review" portions of the course.