Ring homomorphism

Ring monomorphism

Let $𝜑 : 𝑅 \to 𝑆$ be a ring homomorphism. The following statements are equivalent:¹ #m/thm/ring

$𝜑$ is injective;
$𝜑$ is monic;
$k e r 𝜑 = 0$

Proof

#missing/proof

#state/develop | #lang/en | #SemBr

2009. Algebra: Chapter 0, III.2.3, ¶2.4, p. 132 ↩