Remark 5

Tag 06GC, permanent. Cite it as [Bourbaki, Tag 06GC].

Algebra, chapter V, § 1. Prime fields. Characteristic

Let $A$ be a ring not reduced to 0, whose additive group is a torsion-free $\mathbf{Z}$ -module, and put $B = \mathbf{Q} \otimes_{\mathbf{Z}} A$ . The mapping $x \mapsto 1 \otimes x$ of $A$ into $B$ is injective (II, p. 314), hence $A$ is isomorphic to a subring of a ring of characteristic 0.

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

Cited by

Nothing.

Cites

II, p. 314