Remark 2
Tag 0CRD, permanent. Cite it as [Bourbaki, Tag 0CRD].
Commutative Algebra, chapter VIII, § 6. Dimension des anneaux gradués
There exist non-noetherian graded rings H such that dimgr(H) < dim(H) (p. 99, 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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