Bourbaki

Corollary 5

Tag 049U, permanent. Cite it as [Bourbaki, Tag 049U].

Commutative Algebra, chapter II, § 4. Spectra of rings and supports of modules

For f∈Af \in A to satisfy Xf=∅X_f = \varnothing, it is necessary and sufficient that ff be nilpotent.

This follows immediately from Corollary 4.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

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Cites

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Transcribed from the printed volume. Not translated.