I am continuing on my self study in small modules and i have another question: Is it true that $$K_1\leq_s M_1 \text{ and } K_2\leq_s M_2\Leftrightarrow K_1\oplus K_2\leq_s M_1\oplus M_2?$$
Here the notation $$N\leq_s M$$ denotes as usual a small module. I'm pretty sure this follows since if $$N\leq_sM$$ and $f:M\to M'$ is a module morphism then $f(N)\leq_s M'$ which is a fact I've proved. Then my attempt was to work in the two directions using respectively the canonical projections and for the other case the canonical embeddings. In particular I have to convince myself in the case that $$K_1\leq_s M_1 \text{ and } K_2\leq_s M_2\Rightarrow K_1\oplus K_2\leq_s M_1\oplus M_2?$$ Am I correct working with the embeddings?