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.
actually...maybe I'm wrong, now I'm thinking to consider
(c^a)/(d^a)=(c^b)/(d^b) (given since non-zero) ...
I'm thinking if one messes around with this ...I'll get the answer. Does this seem on the right track?
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...