Definition 3

Tag 0026, permanent. Cite it as [Bourbaki, Tag 0026].

Algebra, VIII, p. 31, § 2. The Structure of Modules of Finite Length

A module is called primordial[^1] if its endomorphism ring is local.

By definition, a local ring is not reduced to 0; consequently, a primordial module is nonzero. Moreover, the A-module $A_s$ is primordial if and only if the ring A is local.

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.

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