Is $\mathbb{C}\bigotimes_\mathbb{R}\mathbb{C}\simeq \mathbb{C}\bigotimes_{\mathbb{C}}\mathbb{C}$?
Are $\mathbb{C} \otimes _\mathbb{R} \mathbb{C}$ and $\mathbb{C} \otimes _\mathbb{C} \mathbb{C}$ isomorphic as $\mathbb{R}$-vector spaces?