Answer to Question #16819 in Algebra for sanches

Question

Let I be a right ideal in a polynomial ring A = R[x1, . . . , xn], where R is any ring.
Consider next condition: If f • g = 0 for some nonzero g ∈ A, show that f • r = 0 for some nonzero
r ∈ R. Show that it need not hold if R is an arbitrary ring.