Example

Tag 0DK4, permanent. Cite it as [Bourbaki, Tag 0DK4].

Algebra, chapter IX, § 2. Discriminant d'une forme sesquilinéaire

Let $B$ be an algebra over $A$ which is a free $A$ -module of finite dimension $n$ , $(x_1, \ldots, x_n)$ a basis of $B$ over $A$ , and $m$ an ideal of $A$ . If $h$ denotes the canonical homomorphism of $B$ onto $B/mB$ , $(h(x_1), \ldots, h(x_n))$ is a basis of $B/mB$ over $A/m$ (chap. I, § 6, no 5, prop. 5), and $B/mB$ is isomorphic to $(A/m) \otimes_A B$ . We therefore have

D_{(B/mB)/(A/m)}(h(x_1), \ldots, h(x_n)) = h(D_{B/A}(x_1, \ldots, x_n)).

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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