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

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- Nov 26th 2009, 07:35 AMCarmineCortezunits of polynomial(ring theory)
Prove that if char(R) = n then char(R[x]) = n.

- Nov 26th 2009, 08:40 AMShanks
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.