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...
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...
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.
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...
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
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)...
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?
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...
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¤t=hamming_metric.jpg
and I'm asked to:
http://i1038.photobucket.com/albums/a467/kanye_brown/analysis_1.jpg?t=1306280360 [Broken]
a)...