Generalizations Of Hopfian And Co-Hopfian Modules

This dissertation consists of four chapters. In Chapter 1, we illustrate the back-ground of modules' development, the important roles of the module's theory in the process of algebra and the progress related to Hopfian modules and co-Hopfian modules. In Chapter 2, some basic definitions and important lemmas related to this paper are given. In Chapter 3(4), Hopfian modules (co-Hopfian modules) are generalized in different aspects and the notions ofδ-WH modules,⊕-Hopfian modules, qH modules andχ-qH modules (⊕-co-Hopfian modules, SGCH modules,χ-SGCH modules andχ-qcH modules) are introduced. Some results are obtained, which are more general than usual Hopfian modules (co-Hopfian modules).