Exercise 1, § 6

Let $K$ be a field and $A$ a commutative $K$-algebra. For $A$ to be etale it is necessary and sufficient that there should exist a finite subset $S$ of $A$ generating the $K$-algebra $A$ and such that for all $x \in S$ the subalgebra $K[x]$ generated by $x$ is etale. (If $S$ generates $A$, the $K$-algebra $A$ is isomorphic to a quotient of the tensor product of the $K[x]$, where $x$ runs over $S$.)