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  1. M

    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. M

    Help with complex integral

    Thanks....I think that helps!
  3. M

    Help with complex integral

    No, not sure how to...
  4. M

    Help with complex integral

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

    Help with complex integral

    How can I use these facts to evaluate the integral?
  6. M

    Complex analysis question

    Is it just as simple as applying the Cauchy Integral formula? ie. it follows directly from the CIF?
  7. M

    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. M

    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. M

    Complex analysis question

    Interesting ...I'll reread my notes. Thanks!
  10. M

    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. M

    Hamming metric

    I have a new question. How would I show that the metric space defined by the Hamming metric is complete?
  12. M

    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. M

    What does the following subring of the complex numbers look like

    I'm not sure how to describe polynomials of this form
  14. M

    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
  15. M

    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!
  16. M

    Domain question

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

    Domain question

    interesting...I'll give it a shot -- I know the result but not the name...until now
  18. M

    What does the following subring of the complex numbers look like

    ah...anything with complex #'s... (1+i),x+i, etc..?
  19. M

    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...
  20. M

    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?
  21. M

    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)
  22. M

    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...
  23. M

    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?
  24. M

    Fractional field

    Just know the definition : Fraction field for integral domain = {a/b | a, b are elements of D, b not equal to zero}
  25. M

    Fractional field

    do you know the name of this theorem so I could look it up and see the proof?
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