iterating over quotient ring and polynomial ring

edit

This is something that is indeed missing in Sage. Thanks for your report! I proposed a fixed on ticket #23467. If this ticket is positively reviewed, then the changes will be incorporated into later versions of Sage. And then you will be able to use the exact command you wrote.

In the mean time you can use the following to make the list of nonzero elements in R

sage: P.<v> = PolynomialRing(GF(2))
sage: R.<v> = P.quotient((v^2-v))
sage: T.<x> = PolynomialRing(R)
sage: R_nonzero = [R(p) for i in range(3) for p in P.polynomials(of_degree=i)]

from there it is not hard to build polynomials with coefficients in R.