Understanding how different field extensions interact.
The centerpiece of the chapter, establishing a one-to-one correspondence between subfields of a Galois extension and subgroups of its Galois group. 14.3 Finite Fields: Properties of fields with pnp to the n-th power elements and their cyclic Galois groups. Dummit And Foote Solutions Chapter 14
Introduction to the group of automorphisms of a field that fix a subfield Understanding how different field extensions interact
Including infinite Galois extensions and transcendental extensions. Dummit And Foote Solutions Chapter 14 Dummit And Foote Solutions Chapter 14
Studying the fields generated by roots of unity.