Linear monomorphism

Let $𝑇 : 𝑈 \to 𝑉$ be a $𝕂$ -linear map. The following statements are equivalent:

$𝑇$ is injective;
$𝑇$ is monic in $𝖵 𝖾 𝖼 𝗍 𝕂$ ;
$𝑇$ is split monic in $𝖵 𝖾 𝖼 𝗍 𝕂$ ;
$k e r 𝑇 = {0}$ .

Proof

See Module monomorphism

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