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Citation - WoS: 7
Citation - Scopus: 7
Strongly Radical Supplemented Modules
(Springer Verlag, 2012) Büyükaşık, Engin; Türkmen, Ergül
Zöschinger 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 nonlocal Dedekind domain, an srs-module is the sum of its torsion submodule and the radical submodule. © 2012 Springer Science+Business Media, Inc

Mathematics / Matematik