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Journals / Bitlis Eren Üniversitesi Fen Bilimleri Dergisi / 2026 / Volume: 13 Issue: 1

Rings Characterizations with Mutually SS-Supplemented Modules

Ring Characterizations with Mutually SS-Supplemented Modules

Burcu Nişancı Türkmen(AMASYA ÜNİVERSİTESİ)0000-0001-7900-0529
Zehra Betül Meşeci(AMASYA ÜNİVERSİTESİ)0009-0007-9714-5183
Pages
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Publication Date
2024-03-24
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AI Summary & Key Takeaways

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

It was shown that C=⨁_(ϱ∈Λ ) C_ϱ is a mutually ss-supplemented module which each submodule of C is a fully invariant submodule, for the family of mutually ss-supplemented modules {C_ϱ }_(ϱ∈Λ).

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this text, the notion of mutually ss-supplemented modules characterizes with the help of semiperfect rings.
📊
Key Findings & Data:For this mutually ss-supplemented modules were first classified according to certain properties.
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Conclusion & Impact:It was shown that C=⨁_(ϱ∈Λ ) C_ϱ is a mutually ss-supplemented module which each submodule of C is a fully invariant submodule, for the family of mutually ss-supplemented modules {C_ϱ }_(ϱ∈Λ).
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Semisimple modules · Mutually ss-supplemented modules · Mutual supplements

Abstract

In this text, the notion of mutually ss-supplemented modules characterizes with the help of semiperfect rings. For this mutually ss-supplemented modules were first classified according to certain properties. These features can be listed as follows in the refinable modules, distributive modules, fully invariant submodules and (π-)projective modules. Especially it was proven that each 𝜋-projective mutually ss-supplemented module is amply mutually ss-supplemented. It was obtained that every ss-supplemented refinable module has direct summand which is a mutually ss-supplement in the module. It was shown that C=⨁_(ϱ∈Λ ) C_ϱ is a mutually ss-supplemented module which each submodule of C is a fully invariant submodule, for the family of mutually ss-supplemented modules {C_ϱ }_(ϱ∈Λ).

Özet

In this text, the notion of mutually ss-supplemented modules characterizes with the help of semiperfect rings. For this mutually ss-supplemented modules were first classified according to certain properties. These features can be listed as follows in the refinable modules, distributive modules, fully invariant submodules and (π-)projective modules. Especially it was proven that each 𝜋-projective mutually ss-supplemented module is amply mutually ss-supplemented. It was obtained that every ss-supplemented refinable module has direct summand which is a mutually ss-supplement in the module. It was shown that C=⨁_(ϱ∈Λ ) C_ϱ is a mutually ss-supplemented module which each submodule of C is a fully invariant submodule, for the family of mutually ss-supplemented modules {C_ϱ }_(ϱ∈Λ).

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Cite This Article

Türkmen, B. N., Meşeci, Z. B. (2024). Rings Characterizations with Mutually SS-Supplemented Modules. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, Volume: 13 Issue: 1. https://doi.org/10.17798/bitlisfen.1310501

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References (11)

  1. F. W. Anderson, K. R. Fuller, Graduate Texts in Mathematics. Rings and Categories of Modules, Springer-Verlag, 1992.
  2. T. W. Hungerford, Algebra. Springer Verlag, 502, New York, 1973.
  3. F. Kasch, Modules and Rings. Published for the London Mathematical Society by Academic Press, 372, Teubner, 1982.
  4. E. Kaynar, E. Türkmen and H. Çalışıcı, SS-supplemented modules. Communications Faculty of Sciences. University of Ankara Series A1 Mathematics and Statistics, vol. 69, no. 1, pp. 473-485, 2020.
  5. E. Kaynar, ⨁_ss-supplemented modules. New Trends in Rings and Modules (NTRM 2018), Gebze Technical University. Abstract Book, pp. 3 (June 2018).
  6. B. Koşar and C. Nebiyev, “Tg-supplemented modules,” Miskolc Mathematical Notes, vol. 16, no. 2, pp. 979–986, 2015.
  7. Z. Betül Meşeci, B. Nişancı Türkmen, Mutually SS-Supplemented Modules, 1st Iceans 2022, Proceeding Book, pp 2419-2422, 2022.
  8. A. Ç. Özcan, A. Harmancı, P. F. Smith, “Duo modules,” Glasgow Math. J., vol. 48, pp. 533-545, 2006.
  9. J. J. Rotman, An Introduction to Homological Algebra. Second Edition. Springer Science+Business Media, LLC, 2009.
  10. R. Wisbauer, Foundations of Module and Ring Theory. Gordon and Breach,600, Philadelphia, 1991.
  11. R. Wisbauer, Modules and Algebras: Bimodule Structure on Group Actions and Algebras (Vol. 81). CRC Press, 1996.