I have just started to learn about this today, and though i understand this is probably a very simple question, i'm still quite not sure about it:
is $\mathbb{C}\otimes_{\mathbb{R}}\mathbb{C}=\mathbb{H}$ (when this is a tensor product of algebras)?
my feeling is that the answer is yes. however, I am trying to build the product algebra with the regular construction, and can't seem to get it.
I would greatly appreciate a detailed answer, and not a hint, as i'm very new to this. tahnks alot!