Module homomorphism

Module epimorphism

Let $𝑓 : 𝑀 \to 𝑁$ be an $𝑅$ -module homomorphism. The following statements are equivalent:

$𝑓$ is surjective.
$𝑓$ is an epimorphism in $𝑅 𝖬 𝗈 𝖽$ .
$c o k e r 𝑓 = 0$ .
$𝑓$ is a regular epimorphism.
(with AC) $𝑓$ is a split epimorphism in $𝑅 𝖬 𝗈 𝖽$ .

Proof

#missing/proof

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