I've got another question. I'm currently studying the section concerning small (inessential or superflous, as you wish) submodules: namely we define $N\leq_s M$ if $N\leq M$ and whenever $L\leq M$ is another submodule of $M$ such that $L+N=M$ then necessarily $L=M.$ One of the first question that came to my mind is: is it true the following
$K\leq_s M\leq N\Rightarrow K\leq_s N ?$ I cannot convince myself. If you have references those are welcomed as well.