Lemma 2

Tag 074C, permanent. Cite it as [Bourbaki, Tag 074C].

Algebra, chapter VII, § 4. Finitely generated modules over a principal ideal domain

— The module $A/\mathfrak{a}$ is indecomposable if and only if $\mathfrak{a} \neq A$ and there is no pair $(b, c)$ of ideals of A, distinct from A and $\mathfrak{a}$ , such that $A = b + c$ and $b \cap c = \mathfrak{a}$ .

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

Cited by

Proposition 7, § 4

Cites

Nothing.