Hi

I know how to calculate some easy tensor products like $\mathbb{Z}/m\mathbb{Z} \otimes_{\mathbb{Z}} \mathbb{Z}/n\mathbb{Z}\cong_{\mathbb{Z}} \mathbb{Z}/(m,n)\mathbb{Z} $ or $F[X] \otimes_{F} F[Y] \cong_F F[X,Y]$ or $\mathbb{C} \otimes_\mathbb{R} \mathbb{C} \cong_\mathbb{R} \mathbb{R}^4$ but the reason that I can do this is that the structure of these rings is kinda well-known or they're finitely generated modules I know that continuous real functions over the interval $[0,1]$ form an $\mathbb{R}$-module, so, as a challenge for myself, I tried to find $C([0,1]) \otimes_\mathbb{R} C([0,1])$, but nothing came to my mind. So I thought I would need help and hence that's why I'm writing it here now. I also like to know what $\mathbb{R} \otimes_\mathbb{Q} \mathbb{R}$ looks like, is it algebraically the same as $\mathbb{R}$?

Thanks in advance.