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1. Galois Theory question

Homework Statement Let L/K be a Galois extension with Galois group isomorphic to A4. Let g(x) ϵ K [x] be an irreducible polynomial that is degree 3 that splits in L. Show that the Galois group of g(x) over K is cyclic. Homework Equations The Attempt at a Solution I know...
2. Help with complex integral

Thanks....I think that helps!
3. Help with complex integral

No, not sure how to...
4. Help with complex integral

so the integral would be zero in this case since the residues are -i and i?
5. Help with complex integral

How can I use these facts to evaluate the integral?
6. Complex analysis question

Is it just as simple as applying the Cauchy Integral formula? ie. it follows directly from the CIF?
7. Help with complex integral

Homework Statement Evaluate the integral along the path given: integral(along a(t) of (b^2-1)/(b^2+1) db ) where a(t)=2*e^(it) , 0 <= t <= 2*pi Homework Equations none The Attempt at a Solution I am thinking of using the Residue Theorem. I think there are poles at -i...
8. Ideal help

Homework Statement Show that the ideal J=(a^2, abc, ac^2, c^3) cannot be generated by less than 4 monomials. Homework Equations None The Attempt at a Solution I was thinking of computer a Groebner basis for this (which is what I ended up doing) However, I'm not sure how I can...
9. Complex analysis question

Interesting ...I'll reread my notes. Thanks!
10. Complex analysis question

Homework Statement If an analytic function vanishes on the boundary of a closed disc in its domain , show it vanishes on the full disc Homework Equations CR equations? The Attempt at a Solution Not sure how to start this one.
11. Hamming metric

I have a new question. How would I show that the metric space defined by the Hamming metric is complete?
12. What does the following subring of the complex numbers look like

I was trying to figure out a way of writing things not in the subring, other than the way already written in the question
13. What does the following subring of the complex numbers look like

the things you described like i/(x)*(x+i)
14. What does the following subring of the complex numbers look like

I'm not sure how to describe polynomials of this form
15. What does the following subring of the complex numbers look like

The only difference I can see is things not in the subring don't contain i's, constant terms, or combinations of them
16. Domain question

ah...very useful hint I solved for a before a in ak+lb=1...and that's what made a mess ...this hint 'solved' it - thanks!
17. What does the following subring of the complex numbers look like

...how does knowing this help?
18. Domain question

care to give another hint? I plugged that into one of my equations and just got a big mess
19. Domain question

interesting...I'll give it a shot -- I know the result but not the name...until now
20. What does the following subring of the complex numbers look like

ah...anything with complex #'s... (1+i),x+i, etc..?
21. Domain question

I'm getting then (c^a)*(d^b)-(c^b)*(d^a)=0 I sbustituted in c^b=d^b to get (c^a)*(d^b)-(d^b)*(d^a)=0 but that gets me back to where I started...
22. What does the following subring of the complex numbers look like

oh..I guess constants? 1, 5, etc
23. Domain question

actually...maybe I'm wrong, now I'm thinking to consider (c^a)/(d^a)=(c^b)/(d^b) (given since non-zero) ... I'm thinking if one messes around with this ...I'll get the answer. Does this seem on the right track?
24. What does the following subring of the complex numbers look like

I know (x) is (x) = xR = {r ϵ R | r = at for some t ϵ R} Not sure how to find some element not in (x)
25. Domain question

Homework Statement Let c and d be two non-zero elements of a domain D. If a and b are integers s.t gcd(a,b)=1, a>0, b > 0. If we know c^a=d^a and c^b=d^b, does it follow that c=d? Homework Equations The Attempt at a Solution I'm thinking divinding the two might be...
26. What does the following subring of the complex numbers look like

I mean, because x and x^2 are in (x)
27. What does the following subring of the complex numbers look like

Because they are in (x)?
28. What does the following subring of the complex numbers look like

some elements could be x^3+1/x, x^5+2/x^2, etc...right?
29. What does the following subring of the complex numbers look like

what would happen if the restriction b(x) not in (x) was not there? I'm not sure why that restriction might be there...
30. What does the following subring of the complex numbers look like

Hmm...ok, I didn't know that.