$n$-Hopfian and $n$-co-Hopfian Abelian Groups

Authors : Andrey Chekhlov, Peter Danchev

Pages : 479-489

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Publication Date : 2019-04-01

Article Type : Research

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 $\omega$-Hopfian and $\omega$-co-Hopfian modules over the formal matrix ring.
Keywords : $n$-Hopfian groups, Hopfian groups, $n$-co-Hopfian groups, co-Hopfian groups