Bourbaki

Corollary 1

Tag 045V, permanent. Cite it as [Bourbaki, Tag 045V].

Commutative Algebra, chapter II, § 2. Rings and modules of fractions

For m|s = m'|s' in S^{-1}M, it is necessary and sufficient that there exist t \in S such that t(s'm - sm') = 0.

(m∣s)−(m′∣s′)=(s′m−sm′)/ss′.(m|s) - (m'|s') = (s'm - sm')/ss'.

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

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Transcribed from the printed volume. Not translated.