- 783

- 11

**1. The problem statement, all variables and given/known data**

Construct a splitting s for the polynomial x^3+2x+1 over Z/Z3

**2. Relevant equations**

4=1 Mod 3

:P

**3. 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!