Remark (1)
Tag 04O6, permanent. Cite it as [Bourbaki, Tag 04O6].
Commutative Algebra, chapter V, § 1. Notion of an integral element
If K' is a simple central algebra over K and x \in K' is integral over A, the coefficients of the reduced characteristic polynomial of x (Algebra, Chapter VIII, § 12, no. 3) are integral over A. For there is a power of this polynomial equal to Pc_{K'/K}(x; X) (loc. cit., Proposition 8) and it is sufficient to apply Proposition 17 and no. 3, Proposition 11.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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