abstract algebra -2

• Project ID:

  770435

• Project Type:

  Fixed

• Budget:

  $30-$250 USD
  

Project Description:

please check the questions
i want the solutions in latex and pdf

Additional Project Description:

08/18/2010 at 4:59 EDT:
before hiring
i would like to ask questions...Can someone answer?
i am attaching the solutions too
here is the previous project i have posted
http://www.freelancer.com/projects/Matlab-Mathematica-Mathematics/maths-abstract-algebra.html
let me know in the solution
3b. For a finite degree extension of Q, there are only finitely many roots of unity in K.

You wrote "Define a norm on K by q1^2 + ... + qn^2"

However, this norm is not multiplicative I don't think. So taking the norm of x^j = 1 where x is in K does not imply what you said. Or am I missing something?
4b. For any positive integer n there is an irreducible polynomial in F[x] of degree n, where F is a finite field of size q.

You wrote: x^n + 1 is irreducible for each n.

Where did you use the fact that F is finite? How can you show that each is irreducible?

08/18/2010 at 10:47 EDT:
Please have someone re-work 3b and 4b. The work was not justified, and I'm afraid might be incorrect.
i can pay $5 per subpart for 742+-+2 pdf

Skills required:

Algorithm, Electronics, Engineering, Mathematics, Matlab & Mathematica

Additional Files:

742+-+2.pdf reabstractalgebraescrowfeature%282%29.zip