Example 5
Tag 04KL, permanent. Cite it as [Bourbaki, Tag 04KL].
Commutative Algebra, chapter IV, § 2. Primary decomposition
The powers of any prime ideal are not necessarily primary ideals (Exercise 1). On the other hand, there exist primary ideals which are not powers of prime ideals (Exercise 1).
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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