Field-Theory

Sep 15, 2021 Abstract Algebra 70 min read

Abstract Algebra (8): Galois Theory — The Bridge Between Fields and Groups

The Fundamental Theorem of Galois Theory establishes a perfect correspondence between intermediate fields and subgroups — and settles the ancient question of solvability by radicals.

Sep 13, 2021 Abstract Algebra 66 min read

Abstract Algebra (7): Field Extensions — Building Bigger Number Systems

Algebraic and transcendental extensions, the tower law, minimal polynomials, and splitting fields — the machinery that makes Galois theory possible.