# III. Sample Problems Consider f(x) = x4 - x2 - 2 E Q[x]. Find a sp...

## Transcribed Text

III. Sample Problems Consider f(x) = x4 - x2 - 2 E Q[x]. Find a splitting field K of f(x) over Q. Compute [K : Q]. Suppose F UI K is a field extension of degree p, where p is a prime number. Consider an element a E K \F. (a) Find, with proof, the degree of a over F. (b) Prove that K is a simple extension of F. Let p be a prime number. Find the splitting field of x°P - 1 over F, where: (a) F=Q. (b) F=C. Assume that the characteristic of F is 0. Prove that any degree 2 field extension of F is normal. Let G be the Galois group of x6 - 1 over Q. Prove that G is abelian and identify G (that is, write G as a cyclic group or as a product of cyclic groups).

## Solution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

By purchasing this solution you'll be able to access the following files:
Solution.pdf.

\$25.00
for this solution

PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

### Find A Tutor

View available Abstract Algebra Tutors

Get College Homework Help.

Are you sure you don't want to upload any files?

Fast tutor response requires as much info as possible.