Let p1(t), p2(t) be two polynomials in the F[t] polynomial ring, where F is a field. Let ß1 be a congruence relation for: r(t) ß1 s(t) <==> p1(t)|r(t) - s(t), and ß2 the same for r(t) ß2 s(t) <==> p2(t)|r(t) - s(t).

When will be F[t]/ß1 and F[t]/ß2 isomorph vector spaces. Give necessary and sufficient condition.

Thank you!