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Title: | Strongly Noncosingular Modules | Other Titles: | Güçlü Dual Tekil Olmayan Modüller | Authors: | Alagöz, Yusuf | Advisors: | Büyükaşık, Engin | Keywords: | R-modules | Publisher: | Izmir Institute of Technology | Abstract: | The main purpose of this thesis is to investigate the notion of strongly noncosingular modules. We call a right R-module M strongly noncosingular if for every nonzero right R module N and every nonzero homomorphismf : M → N, Im(f) is not a cosingular (or Radsmall) submodule of N in the sense of Harada. It is proven that (1) A right R-module M is strongly noncosingular if and only if M is coatomic and noncosingular; (2) a right perfect ring R is Artinian hereditary serial if and only if the class of injective right R-modules coincides with the class of (strongly) noncosingular right R-modules; (3) a right hereditary ring R is Max-ring if and only if absolutely coneat right R-modules are strongly noncosingular; (4) a commutative ring R is semisimple if and only if the class of injective R-modules coincides with the class of strongly noncosingular R-modules. | Description: | Thesis (Master)--Izmir Institute of Technology, Mathematics, Izmir, 2014 Includes bibliographical references (leaves: 38-39) Text in English; Abstract: Turkish and English vii, 39 leaves |
URI: | http://hdl.handle.net/11147/4180 |
Appears in Collections: | Master Degree / Yüksek Lisans Tezleri |
Files in This Item:
File | Description | Size | Format | |
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10018486.pdf | MasterThesis | 231.52 kB | Adobe PDF | ![]() View/Open |
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