Example

Tag 0DK1, permanent. Cite it as [Bourbaki, Tag 0DK1].

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

Let $B$ be an algebra over the ring $A$ , such that $B$ is a free $A$ -module of finite dimension $n$ . Then the mapping $(x, y) \to \mathrm{Tr}_{B/A}(xy)$ (Chapter VIII, § 12, no 2) is a bilinear form on $B$ . Given a system $(x_1, \ldots, x_n)$ of $n$ elements of $B$ , the discriminant of this form with respect to this system is called the discriminant of the system $(x_1, \ldots, x_n)$ over $A$ , and is denoted by $D_{B/A}(x_1, \ldots, x_n)$ . Thus

D_{B/A}(x_1, \ldots, x_n) = \det (\mathrm{Tr}_{B/A}(x_ix_j)).

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

Cited by

Nothing.

Cites

Nothing.