Proposition 4

Tag 065Y, permanent. Cite it as [Bourbaki, Tag 065Y].

Let A be a K-algebra admitting a finite basis. For all $a \in A$ , $\mathrm{Pc}_{A/\mathbf{K}}(a; a) = 0$ .

This follows immediately from the Cayley-Hamilton theorem (§ 8, no. 11, Proposition 20).

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

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