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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 48 Issue: 2

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

Andrey Chekhlov0000-0002-9078-128X
Peter Danchev0000-0002-2016-2336
Pages
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Publication Date
2019-04-01
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We also consider and investigate $\omega$-Hopfian and $\omega$-co-Hopfian modules over the formal matrix ring.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:For any natural number $n$ we define and study the two notions of $n$-Hopfian and $n$-co-Hopfian abelian groups.
📊
Key Findings & Data: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.
💡
Conclusion & Impact:We also consider and investigate $\omega$-Hopfian and $\omega$-co-Hopfian modules over the formal matrix ring.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:$n$-Hopfian groups · Hopfian groups · $n$-co-Hopfian 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 $\omega$-Hopfian and $\omega$-co-Hopfian modules over the formal matrix ring.

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Cite This Article

Chekhlov, A., Danchev, P. (2019). $n$-Hopfian and $n$-co-Hopfian Abelian Groups. Hacettepe Journal of Mathematics and Statistics, Volume: 48 Issue: 2. https://ajindex.com/articles/1402816

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