Does $M$-injectivity impy injectivity?

Question

Let $N,M\in R$-mod. We say that $N$ is $M$-injective if for any $L$ submodule of $M$ and any homomorphism $f:L\rightarrow N$ exists a homomorphism $g\colon M\rightarrow N$ that extends $f$.

In the other hand, $N$ is an injective module if for any two $A,B\in R$-mod such that $A\subseteq B$ and $f\in \text{Hom}_R(A,N)$ there exists an element $g\in \text{Hom}_R(B,N)$ that extends $f$.

Am I right that "Every injective module is just a $B$-injective module? Or, am I losing a subtle detail?

Answer 1

$N$ is injective iff it is $M$-injective for all modules $M$.

But it's a theorem (Baer's criterion) that $N$ is injective iff it is $R$-injective.