n-Hopfian and n-co-Hopfian Abelian Groups

Abstract

For any natural number n we define and study the two notions of n-Hopfian and n-co- Hopfian abelian groups. These groups form proper subclasses of the classes of Hopfian and co-Hopfian groups, respectively, and some of their exotic properties are established as well. We also consider and investigate ω-Hopfian and ω-co-Hopfian modules over the formal matrix ring. Mathematics Subject Classification (2010). 20K10, 20K20, 20K21