Strongly radical supplemented modules
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.
English version (Springer): Ukrainian Mathematical Journal 63 (2011), no. 8, pp 1306-1313.
Citation Example: Büyükaşık Е., Türkmen E. Strongly radical supplemented modules // Ukr. Mat. Zh. - 2011. - 63, № 8. - pp. 1140-1146.