I had a question that I don't understand. I was looking through my abstract algebra textbook and I did a couple problem and I got most of the the problems right except for this one: $$R = {(a + b\sqrt[3]{3}}) :a,b\in\mathbb{Q}$$
It might be a dumb question but why is this not a ring?
$(R, +)$ is an abelian group. I double checked and saw that there exist a zero element $0_R\in R$
There exists an inverse such that $a + (-a) = 0_R$
It's associative with the operation +.
In terms of multiplication, it looks like it's associative and distributive as well.
Hints?
