Currently I am studying a proof of the statement that for rings with $B\subseteq A$ we have: Is $A$ a finite $B$-algebra, then $A$ is integral over $B$. Hence every element $x\in A$ satisfies an equation of the form $x^n+b_{n-1}x^{n-1}+\dotso +b_1x+b_0$ with $b_i\in B$. The proof uses a "determin...