I think the possible confusion at 17:38 was about the fact that, when we talk about I^e, it's always w.r.t. some homomorphism. What perhaps seemed most natural here was A->B, so we would say I^e=IB. But, obviously we can just restrict ourselves to any subring such as C, and consider A->C, and thus say I^e=IC, which I think was implicit here.
I think the possible confusion at 17:38 was about the fact that, when we talk about I^e, it's always w.r.t. some homomorphism. What perhaps seemed most natural here was A->B, so we would say I^e=IB. But, obviously we can just restrict ourselves to any subring such as C, and consider A->C, and thus say I^e=IC, which I think was implicit here.
Is x € frac( K[x^3, x^2y, y^3]) ? Anybody please answer!