KaydedilenlerDerginizi ekleyin

Dergiler / 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
Sayfa
—
Yayın Tarihi
2019-04-01
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:For any natural number $n$ we define and study the two notions of $n$-Hopfian and $n$-co-Hopfian abelian groups.
📊
Temel Bulgular & Veri: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.
💡
Sonuç & Katkı:We also consider and investigate $\omega$-Hopfian and $\omega$-co-Hopfian modules over the formal matrix ring.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:$n$-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.

🔖

Bu Makaleye Atıf Yap

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

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (11)

  1. U.F. Albrecht, H.-P. Goeters and W. Wickless, The flat dimension of mixed abelian groups as E-modules, Rocky Mountain J. Math. 25, 569-590, 1995.
  2. A.R. Chekhlov and P.V. Danchev, A generalization of Hopfian abelian groups, Annal. Univ. Sci. Budap. (Math.) 60, 93-109, 2017.
  3. A.R. Chekhlov and P.V. Danchev, A generalization of co-Hopfian abelian groups, Internat. J. Algebra Comput. 27, 351-360, 2017.
  4. L. Fuchs, Infinite Abelian Groups, volumes I and II, Acad. Press, London, 1970 and 1973.
  5. L. Fuchs, Abelian Groups, Springer, Switzerland, 2015.
  6. B. Goldsmith and K. Gong, A note on Hopfian and co-Hopfian abelian groups, Con- temp. Math. 576, 129-136, 2012.
  7. E.V. Kaigarodov, Some classes of Hopfian abelian groups, Fund. Prikl. Mat. 17, 59- 61, 2012.
  8. E.V. Kaigorodov, On two classes of Hopfian abelian groups, Vest. Tomsk University (Math. and Mech.) 22, 22-32, 2013.
  9. E.V. Kaigorodov and P.A. Krylov, On some classes of Hopfian abelian groups and modules, Fundam. Prikl. Math. 20, 61-68, 2015.
  10. P.A. Krylov, A.V. Mikhalev and A.A. Tuganbaev, Endomorphism Rings of Abelian Groups, Kluwer Academic Publishers, Dordrecht, 2003.
  11. P.A. Krylov and A.A. Tuganbaev, Modules over formal matrix rings, J. Math. Sci. 171, 248-295, 2010.