- #1
PsychonautQQ
- 784
- 10
Homework Statement
Construct a splitting s for the polynomial x^3+2x+1 over Z/Z3
Homework Equations
4=1 Mod 3
:P
The Attempt at a Solution
So I'm actually quite confused. There are no roots for x+3+2x+1 over Z/Z3. I am used to constructing splitting fields with polynomials that have coefficients in a field of character zero, for example Q(i) is a splitting field of x+1 over Q.
I guess i am confused because I don't know how to extensions of Z/Z3 will work, will the element I add not be reduced modulus 3? Will the new field have a new character? Any insight appreciated :-)
Thanks PF!