Hopfian And Co-Hopfian Objects

The paper deals with Hopfian , Co-Hopfian, generalized Hopfian and weakly Hopfian objects in categories of modules and rings. In chapter one, Hopficity and Co-Hopficity of modules are discussed. Inspired by the study methods of Hopfian and Co-Hopfian modules, corresponding properties of generalized Hopfian modules and weakly Hopfian modules are given in chapter two. In chapter three, we consider Hopficity of formal power series rings and trivial extension on Hopfian rings, also generalized Hopficity of polynomial rings and direct product of generalized Hopfian rings are discussed.