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The dual notion of $r$-submodules of modules

Yıl 2023, Cilt: 34 Sayı: 34, 112 - 125, 10.07.2023
https://doi.org/10.24330/ieja.1299269

Öz

Let $R$ be a commutative ring with identity and let $M$ be an $R$-module.
A proper submodule $N$ of $M$ is said to be an $r$-submodule if
$am\in N$ with $(0:_Ma)=0$ implies that $m \in N$ for each $a\in R$ and $m\in M$.
The purpose of this paper is to introduce and investigate the dual notion of $r$-submodules of $M$.

Kaynakça

  • D. D. Anderson and T. Dumitrescu, S-Noetherian rings, Comm. Algebra, 30(9) (2002), 4407-4416.
  • A. Anebri, N. Mahdou and Ü. Tekir, Commutative rings and modules that are r-Noetherian, Bull. Korean Math. Soc., 58(5) (2021), 1221-1233.
  • A. Anebri, N. Mahdou and Ü. Tekir, On modules satisfying the descending chain condition on r-submodules, Comm. Algebra, 50(1) (2022), 383-391.
  • H. Ansari-Toroghy and F. Farshadifar, The dual notion of multiplication modules, Taiwanese J. Math., 11(4) (2007), 1189-1201.
  • H. Ansari-Toroghy and F. Farshadifar, Strong comultiplication modules, CMU. J. Nat. Sci., 8(1) (2009), 105-113.
  • H. Ansari-Toroghy and F. Farshadifar, Fully idempotent and coidempotent modules, Bull. Iranian Math. Soc., 38(4) (2012), 987-1005.
  • A. Barnard, Multiplication modules, J. Algebra, 71(1) (1981), 174-178.
  • F. Farshadifar, The dual of the notions n-submodules and j-submodules, Jordan J. Math. Stat., to appear.
  • F. Farshadifar, S-secondary submodules of a module, Comm. Algebra, 49(4) (2021), 1394-1404.
  • S. Koç and Ü. Tekir, r-submodules and sr-submodules, Turkish J. Math., 42(4) (2018), 1863-1876.
  • R. Mohamadian, r-ideals in commutative rings, Turkish J. Math., 39(5) (2015), 733-749.
  • E. S. Sevim, Ü. Tekir and S. Koç, S-Artinian rings and finitely S-cogenerated rings, J. Algebra Appl., 19(3) (2020), 2050051 (16 pp).
  • Ü. Tekir, S. Koç and K. H. Oral, n-ideals of commutative rings, Filomat, 31(10) (2017), 2933-2941.
  • S. Yassemi, Maximal elements of support and cosupport, May 1997, http://streaming.ictp.it/preprints/P/97/051.pdf.
  • S. Yassemi, The dual notion of prime submodules, Arch. Math. (Brno), 37(4) (2001), 273-278.
Yıl 2023, Cilt: 34 Sayı: 34, 112 - 125, 10.07.2023
https://doi.org/10.24330/ieja.1299269

Öz

Kaynakça

  • D. D. Anderson and T. Dumitrescu, S-Noetherian rings, Comm. Algebra, 30(9) (2002), 4407-4416.
  • A. Anebri, N. Mahdou and Ü. Tekir, Commutative rings and modules that are r-Noetherian, Bull. Korean Math. Soc., 58(5) (2021), 1221-1233.
  • A. Anebri, N. Mahdou and Ü. Tekir, On modules satisfying the descending chain condition on r-submodules, Comm. Algebra, 50(1) (2022), 383-391.
  • H. Ansari-Toroghy and F. Farshadifar, The dual notion of multiplication modules, Taiwanese J. Math., 11(4) (2007), 1189-1201.
  • H. Ansari-Toroghy and F. Farshadifar, Strong comultiplication modules, CMU. J. Nat. Sci., 8(1) (2009), 105-113.
  • H. Ansari-Toroghy and F. Farshadifar, Fully idempotent and coidempotent modules, Bull. Iranian Math. Soc., 38(4) (2012), 987-1005.
  • A. Barnard, Multiplication modules, J. Algebra, 71(1) (1981), 174-178.
  • F. Farshadifar, The dual of the notions n-submodules and j-submodules, Jordan J. Math. Stat., to appear.
  • F. Farshadifar, S-secondary submodules of a module, Comm. Algebra, 49(4) (2021), 1394-1404.
  • S. Koç and Ü. Tekir, r-submodules and sr-submodules, Turkish J. Math., 42(4) (2018), 1863-1876.
  • R. Mohamadian, r-ideals in commutative rings, Turkish J. Math., 39(5) (2015), 733-749.
  • E. S. Sevim, Ü. Tekir and S. Koç, S-Artinian rings and finitely S-cogenerated rings, J. Algebra Appl., 19(3) (2020), 2050051 (16 pp).
  • Ü. Tekir, S. Koç and K. H. Oral, n-ideals of commutative rings, Filomat, 31(10) (2017), 2933-2941.
  • S. Yassemi, Maximal elements of support and cosupport, May 1997, http://streaming.ictp.it/preprints/P/97/051.pdf.
  • S. Yassemi, The dual notion of prime submodules, Arch. Math. (Brno), 37(4) (2001), 273-278.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Faranak Farshadıfar Bu kişi benim

Erken Görünüm Tarihi 24 Mayıs 2023
Yayımlanma Tarihi 10 Temmuz 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 34 Sayı: 34

Kaynak Göster

APA Farshadıfar, F. (2023). The dual notion of $r$-submodules of modules. International Electronic Journal of Algebra, 34(34), 112-125. https://doi.org/10.24330/ieja.1299269
AMA Farshadıfar F. The dual notion of $r$-submodules of modules. IEJA. Temmuz 2023;34(34):112-125. doi:10.24330/ieja.1299269
Chicago Farshadıfar, Faranak. “The Dual Notion of $r$-Submodules of Modules”. International Electronic Journal of Algebra 34, sy. 34 (Temmuz 2023): 112-25. https://doi.org/10.24330/ieja.1299269.
EndNote Farshadıfar F (01 Temmuz 2023) The dual notion of $r$-submodules of modules. International Electronic Journal of Algebra 34 34 112–125.
IEEE F. Farshadıfar, “The dual notion of $r$-submodules of modules”, IEJA, c. 34, sy. 34, ss. 112–125, 2023, doi: 10.24330/ieja.1299269.
ISNAD Farshadıfar, Faranak. “The Dual Notion of $r$-Submodules of Modules”. International Electronic Journal of Algebra 34/34 (Temmuz 2023), 112-125. https://doi.org/10.24330/ieja.1299269.
JAMA Farshadıfar F. The dual notion of $r$-submodules of modules. IEJA. 2023;34:112–125.
MLA Farshadıfar, Faranak. “The Dual Notion of $r$-Submodules of Modules”. International Electronic Journal of Algebra, c. 34, sy. 34, 2023, ss. 112-25, doi:10.24330/ieja.1299269.
Vancouver Farshadıfar F. The dual notion of $r$-submodules of modules. IEJA. 2023;34(34):112-25.