Strongly radical supplemented modules |
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Authors: | E Büyükaşık E Türkmen |
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Institution: | 1.Department of Mathematics,Izmir Institute of Technology,Urla,Turkey;2.Department of Mathematics, Faculty of Art and Science,Amasya University,Amasya,Turkey |
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Abstract: | Z?schinger 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. |
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