Thread: units of polynomial(ring theory)

Prove that if char(R) = n then char(R[x]) = n.

Since R[x] contains R, so charR[x] is no less than charR.
If char R is infinite,then it is trivial.
otherwise,Let charR = n, suppose f be any element in R[x], then all the coefficients of nf are 0, since charR=n. So charR[x] is no greater than charR.