Originally Posted by
dabien Suppose we have finite field extensions $\displaystyle B$ and $\displaystyle K$ of $\displaystyle F$ of respective degrees $\displaystyle m$ and $\displaystyle n$, all contained in some larger field $\displaystyle E$. Prove that a domain which is a finite dimentional algebra over a field must be a field, so $\displaystyle B \otimes K$ will be a field if it has no zero divisors.