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Injective Modules and Their Generalizations
(Izmir Institute of Technology, 2018) Demir, Özlem; Büyükaşık, Engin
The main goal of this thesis is to give a survey about some different generalizations of injective modules, namely, C1, C2, C3-conditions and the modules which satisfy the simple versions of these conditions. A right R-module M is called simple-directinjective if every simple submodule which is isomorphic to a direct summand of M is itself a summand, or if the direct sum of any two simple summands whose intersection is zero is a direct summand of M. Firstly, various basic properties and some characterizations of these modules are presented. The relation between simple-direct-injective modules and C3-modules is exhibited. Also, we obtain the structure of simple-direct-injective modules over the ring of integers and over semilocal rings. It is shown that over a commutative ring every nonsingular module is simple-direct-injective.

Master Degree / Yüksek Lisans Tezleri