Recent content by Metric_Space

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...

Thanks...I think that helps!

No, not sure how to...

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

How can I use these facts to evaluate the integral?

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

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...

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...

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

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.

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

I was trying to figure out a way of writing things not in the subring, other than the way already written in the question

the things you described like i/(x)*(x+i)

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

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