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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

    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...
  3. 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...
  4. 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.
  5. 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...
  6. M

    What does the following subring of the complex numbers look like

    Homework Statement What does the following subring of the complex numbers look like: {a(x)/b(x) | b(x) ϵ C[x], b(x) is not a member of (x)} ? Homework Equations The Attempt at a Solution
  7. M

    Idea question

    Homework Statement Why are prime ideals so important? Homework Equations The Attempt at a Solution
  8. M

    Fractional field

    How would I go about finding the fraction field of Z[1/2]?
  9. M

    Analysis help

    Homework Statement Let X=R^2 and the distance be the usual Euclidean distance. If C and D are non-empty sets of R^2 and we have: C+D := {y ϵ R^2 | there exists c ϵ C and dϵD s.t c+d = y} A) What is C+D if the open balls are C= ball((0.5,0.5);2) and D=ball((0.5,2.5);1) B) Same as A)...
  10. M

    Prime ideal question (abstract algebra)

    Homework Statement Let D = Z[sqrt(10)], and let P be the ideal (2,sqrt(10)) 10). Prove that P is a prime ideal of D. Homework Equations The Attempt at a Solution Not sure where to start. I think elements are of the for a+b*sqrt(10), a,b integers. Any hints as to what to do next?
  11. M

    Help with complex analysis

    Homework Statement i) Find a suitable formula for log z when z lies in the half-plane K that lies above the x-axis, and from that show log is holomorphic on K ii) Find a suitable formula for log z when z lies in the half-plane L that lies below the x-axis, and from that show log is...
  12. M

    Hamming metric

    Homework Statement I'm stuck on how to start this. The Hammin metric is define: http://s1038.photobucket.com/albums/a467/kanye_brown/?action=view&current=hamming_metric.jpg and I'm asked to: http://i1038.photobucket.com/albums/a467/kanye_brown/analysis_1.jpg?t=1306280360 [Broken] a)...
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