Strictly Invariant Submodules

Abstract

If M is an R-module, we study the submodules K ≤ M with the property that K is invariant with respect to all monomorphisms K → M . Such submodules are called strictly invariant. For the case of Z-modules (i.e. Abelian groups) we prove that in many situations these submodules are invariant with respect to all homomorphisms K → M , submodules which were called strongly invariant. * 2010