WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7150
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Article Citation - WoS: 7Citation - Scopus: 7Strongly Radical Supplemented Modules(Springer Verlag, 2012) Büyükaşık, Engin; Türkmen, ErgülZöschinger 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, IncArticle Citation - WoS: 28Citation - Scopus: 29Rad-Supplemented Modules(Universita di Padova, 2010) Büyükaşık, Engin; Mermut, Engin; Özdemir, SalahattinLet τ be a radical for the category of left R-modules for a ring R. If M is a τ-coatomic module, that is, if M has no nonzero τ-torsion factor module, then τ(M) is small in M. If V is a τ-supplement in M, then the intersection of V and τ(M) is τ(V). In particular, if V is a Rad-supplement in M, then the intersection of V and Rad(M) is Rad(V). A module M is τ-supplemented if and only if the factor module of M by P τ(M) is τ-supplemented where P τ(M) is the sum of all τ-torsion submodules of M. Every left R-module is Rad-supplemented if and only if the direct sum of countably many copies of R is a Rad-supplemented left R-module if and only if every reduced left R-module is supplemented if and only if R/P(R) is left perfect where P(R) is the sum of all left ideals I of R such that Rad I = I. For a left duo ring R, R is a Rad-supplemented left R-module if and only if R/P(R) is semiperfect. For a Dedekind domain R, an R-module M is Rad-supplemented if and only if M/D is supplemented where D is the divisible part of M.