MAT347Y1: Groups, Rings and Fields

Hours: 
72L/24T

Groups, subgroups, quotient groups, Sylow theorems, Jordan-Hölder theorem, finitely generated abelian groups, solvable groups. Rings, ideals, Chinese remainder theorem; Euclidean domains and principal ideal domains: unique factorization. Noetherian rings, Hilbert basis theorem. Finitely generated modules. Field extensions, algebraic closure, straight-edge and compass constructions. Galois theory, including insolvability of the quintic.

Prerequisite: 

MAT257Y1/​(MAT247H1 and permission of the instructor)

Distribution Requirements: 
Science
Breadth Requirements: 
The Physical and Mathematical Universes (5)