: Solutions demonstrate using Cardano's formula to find the roots of
I should break down the main topics in Chapter 14. Let me recall: field extensions, automorphisms, splitting fields, separability, Galois groups, the Fundamental Theorem of Galois Theory, solvability by radicals. Each of these sections would have exercises. The solutions chapter would cover all these. Dummit And Foote Solutions Chapter 14
Problem (paraphrased): Let $K$ be the splitting field of $x^4-2$ over $\mathbbQ$. Find all intermediate subfields $E$ with $[E:\mathbbQ]=4$ and determine which are Galois over $\mathbbQ$. : Solutions demonstrate using Cardano's formula to find
Determine the Galois group of $x^3 - 2$ over $\mathbbQ$ and find the lattice of intermediate fields. the Fundamental Theorem of Galois Theory