Free chapterTry everything here: cards, proofs and practice. Sign up free to save your progress and unlock all 5 chapters.Sign up free

GALOIS · 1

Field extensions

11 concepts · 19 questions

← Back to cards1 / 4

GALOISStep●○○○○new1 Field extensions

Step 1 of 3 towards a full problem

The problem

Let $f = x^4 + 1$ over $\mathbb{Q}$ . (a) Show $f$ is irreducible. (b) Find its roots and splitting field. (c) Find the degree of the splitting field.

Prove irreducibility.