Definition 1

Let $\mathbf{A}$ be a commutative algebra over a field $K$. Then $A$ is said to be separable over $K$, or also a separable $K$-algebra if the ring $L \otimes_K \mathbf{A}$ is reduced for every extension $L$ of $K$.

Every separable algebra is clearly reduced. For a partial converse see Th. 3 (V, p. 125).