Remark 1

Tag 0DN8, permanent. Cite it as [Bourbaki, Tag 0DN8].

Algebra, chapter IX, § 8. Types de formes quadratiques

It is clear that, if $a$ is an element of $A^*$ , one has

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a . (TT') = (a . T)T' = T(a . T')

whatever the elements $T, T'$ of $\mathfrak{B}$ may be. It will moreover be observed that one has $a . T = T_a T$ , denoting by $T_a$ the type of the quadratic form $aQ_1$ over $A$ .

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

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Cites

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