Araştırma Makalesi
BibTex RIS Kaynak Göster

Ring Characterizations with Mutually SS-Supplemented Modules

Yıl 2024, , 30 - 34, 24.03.2024
https://doi.org/10.17798/bitlisfen.1310501

Öz

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).

Kaynakça

  • [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.

Rings Characterizations with Mutually SS-Supplemented Modules

Yıl 2024, , 30 - 34, 24.03.2024
https://doi.org/10.17798/bitlisfen.1310501

Öz

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).

Kaynakça

  • [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.
Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Bulanık Hesaplama
Bölüm Araştırma Makalesi
Yazarlar

Burcu Nişancı Türkmen 0000-0001-7900-0529

Zehra Betül Meşeci 0009-0007-9714-5183

Erken Görünüm Tarihi 21 Mart 2024
Yayımlanma Tarihi 24 Mart 2024
Gönderilme Tarihi 6 Haziran 2023
Kabul Tarihi 21 Şubat 2024
Yayımlandığı Sayı Yıl 2024

Kaynak Göster

IEEE B. Nişancı Türkmen ve Z. B. Meşeci, “Rings Characterizations with Mutually SS-Supplemented Modules”, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, c. 13, sy. 1, ss. 30–34, 2024, doi: 10.17798/bitlisfen.1310501.



Bitlis Eren Üniversitesi
Fen Bilimleri Dergisi Editörlüğü

Bitlis Eren Üniversitesi Lisansüstü Eğitim Enstitüsü        
Beş Minare Mah. Ahmet Eren Bulvarı, Merkez Kampüs, 13000 BİTLİS        
E-posta: fbe@beu.edu.tr