
Tensorial Product
Hi,
I have to solve this question, I appreciate your help.
The ring $\displaystyle \mathbb{C} \otimes_{\mathbb{R}} \mathbb{C}$ isn't an Integral Domain
The multiplication operation in this ring is the usual complex multiplication by components.
Thanks

let $\displaystyle x = 1 \otimes i  i \otimes 1$ and $\displaystyle y = 1 \otimes i + i \otimes 1$. what is $\displaystyle xy$? note that both $\displaystyle x$ and $\displaystyle y$ are nonzero because $\displaystyle \{1,i\}$ is linearly independent over $\displaystyle \mathbb{R}$.
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