Corollary 1

Tag 05KG, permanent. Cite it as [Bourbaki, Tag 05KG].

Algebra, chapter II, § 1. Modules

Let $u : E \to F$ be a linear mapping, S a subset of $E$ and $M$ the submodule of $E$ generated by $S$ . Then $u(M)$ is the submodule of $F$ generated by $u(S)$ .

In particular, the image under $u$ of any finitely generated submodule of $E$ is a finitely generated submodule of $F$ .

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

Cited by

Proposition 22, § 1

Cites

Nothing.