On strongly coseparable modules

Abstract A module M is called $$\mathfrak {s}$$ s -coseparable if for every nonzero submodule U of such that / finitely generated, there exists a direct summand V $$V \subseteq U$$ V ⊆ U and generated. It shown non-finitely generated free but not, in general, -coseparable. We prove the class modules over right noetherian ring closed under finite sums. show commutative rings R which cyclic -module exactly von Neumann regular rings. Some examples are provided.