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`https://hdl.handle.net/11147/4182`

Title: | Homological objects of proper classes generated by simple modules |

Other Titles: | Basit modüller ile üretilen öz sınıfların homolojik nesneleri |

Authors: | Durğun, Yılmaz |

Advisors: | Büyükaşık, Engin |

Keywords: | General module theory Associative rings Homological algebra Proper classes Injective modules |

Publisher: | Izmir Institute of Technology |

Abstract: | The main purpose of this thesis is to study some classes of modules determined by neat, coneat and s-pure submodules. A right R-module M is called neat-flat (resp. coneat-flat) if the kernel of any epimorphism Y → M → 0 is neat (resp. coneat) in Y. A right R-module M is said to be absolutely s-pure if it is s-pure in every extension of it. If R is a commutative Noetherian ring, then R is C-ring if and only if coneat-flat modules are flat. A commutative ring R is perfect if and only if coneat-flat modules are projective. R is a right Σ -CS ring if and only if neat-flat right R-modules are projective. R is a right Kasch ring if and only if injective right R-modules are neat-flat if and only if the injective hull of every simple right R-module is neat-flat. If R is a right N-ring, then R is right Σ -CS ring if and only if pure-injective neat-flat right R-modules are projective if and only if absolutely s-pure left R-modules are injective and R is right perfect. A domain R is Dedekind if and only if absolutely s-pure modules are injective. It is proven that, for a commutative Noetherian ring R, (1) neat-flat modules are flat if and only if absolutely s-pure modules are absolutely pure if and only if R A × B, wherein A is QF-ring and B is hereditary; (2) neat-flat modules are absolutely s-pure if and only if absolutely s-pure modules are neat-flat if and only if R A × B, wherein A is QF-ring and B is Artinian with J2(B) = 0. |

Description: | Thesis (Doctoral)--Izmir Institute of Technology, Mathematics, Izmir, 2014 Includes bibliographical references (leaves: 67-72) Text in English; Abstract: Turkish an English ix, 72 leaves |

URI: | http://hdl.handle.net/11147/4182 |

Appears in Collections: | Phd Degree / Doktora |

###### Files in This Item:

File | Description | Size | Format | |
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10018485.pdf | DoctoralThesis | 266.87 kB | Adobe PDF | View/Open |

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