Zoschinger studied modules whose radicals have supplements and called these modules radical supplemented.
Motivated by this, we call a module strongly radical supplemented (briefly srs) if every submodule containing
the radical has a supplement. We prove that every (finitely generated) left module is an srs-module if and
only if the ring is left (semi)perfect. Over a local Dedekind domain, srs-modules and radical supplemented
modules coincide. Over a no-local Dedekind domain, an srs-module is the sum of its torsion submodule and
the radical submodule.
