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?