Baer's Criterion

Theorem
Let $R$ be a ring.

Let $M$ be a left $R$-module.

Then $M$ is injective the following condition holds:
 * For all left ideals $I$ of $R$ with inclusion map $\iota : I \to R$ and all $R$-module homomorphisms $f : I \to M$, there is an $R$-module homomorphism $\tilde f : R \to M$ with $\tilde f \circ \iota = f$.