Example 2

Tag 0037, permanent. Cite it as [Bourbaki, Tag 0037].

Algebra, VIII, p. 45, § 3. Simple Modules

Let A be a principal ideal domain (VII, §1, No. 1, p. 1, Definition 1) that is not a field. For every irreducible element $\pi$ of A, the A-module $A_s/(\pi )$ is simple, and every simple A-module is isomorphic to such a module (VII, §4, No. 8, p. 25, Remark 4). For $n\geqslant 2$ , the A-module $A_s/(\pi^n)$ is indecomposable (VII, §4, No. 8, p. 24, Proposition 8) but not simple.

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

Cited by

Nothing.

Cites

VII, §4, No. 8, p. 25, Remark 4 not in this corpus
VII, §4, No. 8, p. 24, Proposition 8 not in this corpus