Corollary 1

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

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

Let $A$ be a ring, $S$ a subset of $A$ and $u$ an injective homomorphism of $A$ to a ring $B$ such that the elements of $u(S)$ are invertible in $B$ . The unique homomorphism $u'$ of $A[S^{-1}]$ to $B$ such that $u' \circ i_A^S = u$ is then injective.

This is an immediate consequence of Proposition 2 and Remark 6.

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

Cited by

Corollary 2, § 2
Corollary 4, § 2
Proposition 10, § 2

Cites

Proposition 2