Rings Whose Certain Modules are Dual Self-CS-Baer

Nuray Eroğlu

doi:10.36753/mathenot.1461857

Araştırma Makalesi

Rings Whose Certain Modules are Dual Self-CS-Baer

Yıl 2024, , 113 - 118, 24.09.2024

Nuray Eroğlu

https://doi.org/10.36753/mathenot.1461857

Öz

In this work, we characterize some rings in terms of dual self-CS-Baer modules (briefly, ds-CS-Baer modules). We prove that any ring $R$ is a left and right artinian serial ring with $J^2(R)=0$ iff $R\oplus M$ is ds-CS-Baer for every right $R$-module $M$. If $R$ is a commutative ring, then we prove that $R$ is an artinian serial ring iff $R$ is perfect and every $R$-module is a direct sum of ds-CS-Baer $R$-modules. Also, we show that $R$ is a right perfect ring iff all countably generated free right $R$-modules are ds-CS-Baer.

Anahtar Kelimeler

Dual self-CS-Baer module, Harada ring, Lifting module, Perfect ring, QF-ring, Serial ring

Kaynakça

[1] Clark, J., Lomp, C., Vanaja, N., Wisbauer, R.: Lifting Modules: Supplements and Projectivity in Module Theory. Frontiers in Mathematics, Birkhäuser (2006).
[2] Mohamed, S. H., Müller, B. J.: Continuous and Discrete Modules. London Mathematical Society Lecture Note Series, Vol. 147, Cambridge University Press (1990).
[3] Crivei, S., Keskin Tütüncü, D., Radu, S. M., Tribak, R.: CS-Baer and dual CS-Baer objects in abelian categories. Journal of Algebra and Its Applications. 22(10), 2350220 (2023).
[4] Anderson, F. W., Fuller, K. R.: Rings and Categories of Modules. 2nd edition, Springer-Verlag, New York (1992).
[5] Crivei, S., Radu, S. M.: CS-Rickart and dual CS-Rickart objects in abelian categories. Bulletin of Belgian Mathematical Society-Simon Stevin. 29(1), 99–122 (2022).
[6] Tribak, R.: Dual CS-Rickart modules over Dedekind domains. Algebras and Representation Theory. 23, 229–250 (2020).
[7] Keskin, D., Smith, P. F., Xue,W.: Rings whose modules are ⊕-supplemented. Journal of Algebra. 218(2), 470–487 (1999).
[8] Büyükaşık, E., Lomp, C.: On recent generalization of semiperfect rings. Bulletin of the Australian Mathematical Society. 78(2), 317–325 (2008).
[9] Warfield, R. B.: Serial rings and finitely presented modules. Journal of Algebra. 37(2), 187–222 (1975).
[10] Brandal, W.: Commutative Rings Whose Finitely Generated Modules Decompose. Lecture Notes in Mathematics, Vol. 723, Springer-Verlag, Berlin (1979).
[11] Harmancı, A., Keskin, D., Smith, P. F.: On ⊕-supplemented modules. Acta Mathematica Hungarica. 83 , 161–169 (1999).

Yıl 2024, , 113 - 118, 24.09.2024

Nuray Eroğlu

https://doi.org/10.36753/mathenot.1461857

Öz

Kaynakça

[1] Clark, J., Lomp, C., Vanaja, N., Wisbauer, R.: Lifting Modules: Supplements and Projectivity in Module Theory. Frontiers in Mathematics, Birkhäuser (2006).
[2] Mohamed, S. H., Müller, B. J.: Continuous and Discrete Modules. London Mathematical Society Lecture Note Series, Vol. 147, Cambridge University Press (1990).
[3] Crivei, S., Keskin Tütüncü, D., Radu, S. M., Tribak, R.: CS-Baer and dual CS-Baer objects in abelian categories. Journal of Algebra and Its Applications. 22(10), 2350220 (2023).
[4] Anderson, F. W., Fuller, K. R.: Rings and Categories of Modules. 2nd edition, Springer-Verlag, New York (1992).
[5] Crivei, S., Radu, S. M.: CS-Rickart and dual CS-Rickart objects in abelian categories. Bulletin of Belgian Mathematical Society-Simon Stevin. 29(1), 99–122 (2022).
[6] Tribak, R.: Dual CS-Rickart modules over Dedekind domains. Algebras and Representation Theory. 23, 229–250 (2020).
[7] Keskin, D., Smith, P. F., Xue,W.: Rings whose modules are ⊕-supplemented. Journal of Algebra. 218(2), 470–487 (1999).
[8] Büyükaşık, E., Lomp, C.: On recent generalization of semiperfect rings. Bulletin of the Australian Mathematical Society. 78(2), 317–325 (2008).
[9] Warfield, R. B.: Serial rings and finitely presented modules. Journal of Algebra. 37(2), 187–222 (1975).
[10] Brandal, W.: Commutative Rings Whose Finitely Generated Modules Decompose. Lecture Notes in Mathematics, Vol. 723, Springer-Verlag, Berlin (1979).
[11] Harmancı, A., Keskin, D., Smith, P. F.: On ⊕-supplemented modules. Acta Mathematica Hungarica. 83 , 161–169 (1999).

Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Konular	Uygulamalı Matematik (Diğer)
Bölüm	Articles
Yazarlar	Nuray Eroğlu 0000-0002-0780-2247
Erken Görünüm Tarihi	30 Nisan 2024
Yayımlanma Tarihi	24 Eylül 2024
Gönderilme Tarihi	30 Mart 2024
Kabul Tarihi	30 Nisan 2024
Yayımlandığı Sayı	Yıl 2024

Kaynak Göster

APA	Eroğlu, N. (2024). Rings Whose Certain Modules are Dual Self-CS-Baer. Mathematical Sciences and Applications E-Notes, 12(3), 113-118. https://doi.org/10.36753/mathenot.1461857
AMA	Eroğlu N. Rings Whose Certain Modules are Dual Self-CS-Baer. Math. Sci. Appl. E-Notes. Eylül 2024;12(3):113-118. doi:10.36753/mathenot.1461857
Chicago	Eroğlu, Nuray. “Rings Whose Certain Modules Are Dual Self-CS-Baer”. Mathematical Sciences and Applications E-Notes 12, sy. 3 (Eylül 2024): 113-18. https://doi.org/10.36753/mathenot.1461857.
EndNote	Eroğlu N (01 Eylül 2024) Rings Whose Certain Modules are Dual Self-CS-Baer. Mathematical Sciences and Applications E-Notes 12 3 113–118.
IEEE	N. Eroğlu, “Rings Whose Certain Modules are Dual Self-CS-Baer”, Math. Sci. Appl. E-Notes, c. 12, sy. 3, ss. 113–118, 2024, doi: 10.36753/mathenot.1461857.
ISNAD	Eroğlu, Nuray. “Rings Whose Certain Modules Are Dual Self-CS-Baer”. Mathematical Sciences and Applications E-Notes 12/3 (Eylül 2024), 113-118. https://doi.org/10.36753/mathenot.1461857.
JAMA	Eroğlu N. Rings Whose Certain Modules are Dual Self-CS-Baer. Math. Sci. Appl. E-Notes. 2024;12:113–118.
MLA	Eroğlu, Nuray. “Rings Whose Certain Modules Are Dual Self-CS-Baer”. Mathematical Sciences and Applications E-Notes, c. 12, sy. 3, 2024, ss. 113-8, doi:10.36753/mathenot.1461857.
Vancouver	Eroğlu N. Rings Whose Certain Modules are Dual Self-CS-Baer. Math. Sci. Appl. E-Notes. 2024;12(3):113-8.