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

Year 2019, Volume: 48 Issue: 2, 479 - 489, 01.04.2019

Andrey Chekhlov Peter Danchev

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

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