CH 3 - Splitting Fields and Normal Extensions

Question 1

Define a splitting field for g over F.

State a theorem on existence of splitting fields.

Answer 1

Question 2

State a lemma on isomorphisms and extensions of isomorphisms of fields.

State a corollary on the uniqueness of splitting fields.

Answer 2

Question 3

Define a normal extension.

State a theorem on normal extensions vs splitting fields.

State a lemma on F<=L<=K and normal extensions.

Answer 3

Question 4

Define when g is seperable over F.

State a differential result for f = X^p + 1 over a field of characteristic p

State a lemma linking formal differentiation and the concept of separability.

Answer 4

Question 5

State a lemma on the Complex field C and derivatives.

State and prove a proposition on fields of characterisic 0.

Answer 5

Question 6

Define a separable extension.

State a corollary on separable extensions.

State a lemma on intermediate extensions of separable extensions.

Answer 6