Unit · year 3
MU-303 · Rings, Fields & Galois Theory
Threads structure6 theorems
From factorisation in rings to the symmetry theory that settles the quintic.
Theorems in this unit
T-089
Every PID is a UFD
Principal ideal domains have unique factorisation.
T-090
Eisenstein's criterion
A prime-based test for irreducibility of polynomials.
T-091
The tower law
Degrees of field extensions multiply.
T-092
The fundamental theorem of Galois theory
Subfields correspond to subgroups of the Galois group.
T-093
Classification of finite fields
There is exactly one field of each prime-power order.
T-094
Insolvability of the quintic
No general radical formula solves degree-five equations.