Strictly invariant submodules

Abstract

If $M$ is an $R$-module, we study the submodules $K\le M$ with the property that $K$ is invariant with respect to all monomorphisms $K\to M$. Such submodules are called \textsl{strictly invariant}. For the case of -modules (i.e. Abelian groups) we prove that in many situations these submodules are invariant with respect to all homomorphisms , submodules which were called \textsl{strongly invariant}.

preprint version; the final version will be published by Mediterranean J. of Math