(a) Let I be a nonzero ideal of R[x] and p(x) a nonzero polynomial of least degree in I with leading coefficient a. If ∫(x) ϵ R[x] and a^m∫(x) = 0, then a^m-1p(x}f(x} = 0.

(b) If a ring R has no nonzero nil ideals (in particular, if R is semi simple), then R[xJ is semi simple. 

(c) There exist rings R such that R[x] is semi simple, but R is not.