Recent content by Metric_Space

  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
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