Definition 2

Tag 04JS, permanent. Cite it as [Bourbaki, Tag 04JS].

Commutative Algebra, chapter IV, § 1. Prime ideals associated with a module

Given an $A$ -module $M$ , an endomorphism $u$ of $M$ is called almost nilpotent if, for all $x \in M$ , there exists an integer $n(x) > 0$ such that $u^{n(x)}(x) = 0$ .

If $M$ is finitely generated, every almost nilpotent endomorphism is nilpotent.

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

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