# Recent content by Metric_Space

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