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Title: Strongly noncosingular modules
Other Titles: Güçlü dual tekil olmayan modüller
Authors: Büyükaşık, Engin
Alagöz, Yusuf
Keywords: R-modules
Issue Date: 2014
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
Appears in Collections:Master Degree / Yüksek Lisans Tezleri

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