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On Generalization of Hopfian Modules
(Izmir Institute of Technology, 2018) Yaman, Mehmet; Büyükaşık, Engin
The notion of Hopfian modules are defined as a generalization of modules of finite length as the modules whose surjective endomorphisms are isomorphisms. These modules and several generalizations of them are extensively studied in the literature. The aim of this thesis is to review some known results and extends some results about generalized Hopfian and weakly Hopfian modules. It is shown that a module is Hopfian if and only if it is both generalized Hopfian and weakly Hopfian. Torsion-free abelian groups are weakly Hopfian. Any nonsingular uniform module is weakly Hopfian. Direct summands of weakly Hopfian modules is weakly Hopfian. It is shown that direct sum weak Hopfian modules is not necessarily weakly Hopfian.

Master Degree / Yüksek Lisans Tezleri