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/(85% in MAT247H1/MAT247H5)
Distribution Requirements
Science
Breadth Requirements
The Physical and Mathematical Universes (5)