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`https://hdl.handle.net/11147/2523`

Title: | Rad-supplemented modules |

Authors: | Büyükaşık, Engin Mermut, Engin Özdemir, Salahattin |

Keywords: | Relative homological algebra R-modules General module theory Local rings |

Issue Date: | 2010 |

Publisher: | Universita di Padova |

Source: | Büyükaşık, E., Mermut, E., and Özdemir, S. (2010). Rad-supplemented modules. Mathematical Journal of the University of Padova, 124, 157-177. doi:10.4171/RSMUP/124-10 |

Abstract: | Let 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. |

URI: | http://doi.org/10.4171/RSMUP/124-10 http://hdl.handle.net/11147/2523 |

ISSN: | 0041-8994 |

Appears in Collections: | Mathematics / Matematik Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection |

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