Example 2
Tag 00CU, permanent. Cite it as [Bourbaki, Tag 00CU].
Algebra, VIII, p. 183, § 11. Grothendieck Groups
The set of classes of finitely generated A-modules is additive. If the ring A is Noetherian, then this set is hereditary (VIII, p. 3, Proposition 3 and VIII, p. 7, Proposition 4).
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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