Araştırma Makalesi
BibTex RIS Kaynak Göster

The Source of $\Gamma$-Primeness on $\Gamma$-Rings

Yıl 2024, Cilt: 12 Sayı: 1, 36 - 42, 28.01.2024

Didem Yeşil Rasie Mekera

https://doi.org/10.36753/mathenot.1389757

Öz

The source of the primeness texture is a skeleton that generalizes traditional prime rings. In this context, our primary aim in this study is to describe the source of $\Gamma$-primeness in $\Gamma$-rings not included in the literature.
This work's purpose is to generalize the concept of the source of primeness to a $\Gamma$-ring. In this study, the characteristics provided by the defined concept are also discussed, and the results achieved are exemplified.

Anahtar Kelimeler

Prime $\Gamma$-ideal Source of $\Gamma$-primeness $\Gamma$-ring

Kaynakça

  • [1] Nobusawa, N.: On a generalization of the ring theory. Osaka Journal of Mathematics. 1, 81-89 (1964).
  • [2] Barnes,W.: On the 􀀀-rings of Nobusawa. Pacific Journal of Mathematics. 18(3), 411-422 (1966).
  • [3] Kyuno, S.: On prime 􀀀-rings. Pacific Journal of Mathematics. 75(1), 185-190 (1978).
  • [4] Kyuno, S.: Prime ideals in 􀀀-rings. Pacific Journal of Mathematics. 98(2), 375-379 (1982).
  • [5] Ravisankar, T. S., Shukla, U. S.: Structure of 􀀀-rings. Pacific Journal of Mathematics. 82(2), 537-559 (1979).
  • [6] Ardakani, L. K., Davvaz, B., Huang, S.: On derivations of prime and semi-prime Gamma rings. Boletim da Sociedade Paranaense de Matemática. 37(2), 157-166 (2019).
  • [7] Kyuno, S., Nobusawa, N., Smith, M. B.: Regular gamma rings. Tsukuba journal of mathematics. 11(2), 371-382 (1987).
  • [8] Estaji, A. A., Khorasani, A. S., Baghdari, S.: Multiplication Ideals in Gamma-rings. Journal of Hyperstructures. 2(1), (2013).
  • [9] Aydın, N., Demir, Ç., Karalarlıo˘glu Camcı, D.: The source of semiprimeness of rings. Communications of the Korean Mathematical Society. 33(4), 1083-1096 (2018).
  • [10] Arslan, O., Düzkaya, N.: The Source of Semi-Primeness of 􀀀-Rings. Fundamentals of Contemporary Mathematical Sciences. 4(2), 87-95 (2023).
  • [11] Karalarlıoglu Camcı, D.: Source of Semiprimeness and Multiplicative (generalized) Derivations in Rings. PhD dissertation. Çanakkale Onsekiz Mart University, Ç, (2017).
  • [12] Yeşil, D., Karalarlıoğlu Camcı, D.: The Source of Primeness of Rings. Journal of New Theory. 41, 100-104 (2022).
  • [13] Tabatabaee, Z. S., Roodbarylor, T.: The Construction of Fraction Gamma Rings and Local Gamma Rings by Using Commutative Gamma Rings. Journal of Mathematical Extension. 12(1), 73-86 (2018).
  • [14] Dükel, K. Ç., Çeven, Y.: Additivity of Multiplicative Isomorphisms in Gamma Rings. Palestine Journal of Mathematics. 6, (2017).
  • [15] Paul, R.: On various types of ideals of 􀀀-rings and the corresponding operator rings. International Journal of engineering Research and Applications. 5(8), 95-98 (2015).
  • [16] Adham Abdallah, Q.: Derivations on 􀀀-Rings, Prime 􀀀-Rings and Semiprime 􀀀-Rings. Doctoral Thesis. Faculty of Graduate Studies, Hebron University, Hebron, Palestine. (2017).

Yıl 2024, Cilt: 12 Sayı: 1, 36 - 42, 28.01.2024

Didem Yeşil Rasie Mekera

https://doi.org/10.36753/mathenot.1389757

Öz

Kaynakça

  • [1] Nobusawa, N.: On a generalization of the ring theory. Osaka Journal of Mathematics. 1, 81-89 (1964).
  • [2] Barnes,W.: On the 􀀀-rings of Nobusawa. Pacific Journal of Mathematics. 18(3), 411-422 (1966).
  • [3] Kyuno, S.: On prime 􀀀-rings. Pacific Journal of Mathematics. 75(1), 185-190 (1978).
  • [4] Kyuno, S.: Prime ideals in 􀀀-rings. Pacific Journal of Mathematics. 98(2), 375-379 (1982).
  • [5] Ravisankar, T. S., Shukla, U. S.: Structure of 􀀀-rings. Pacific Journal of Mathematics. 82(2), 537-559 (1979).
  • [6] Ardakani, L. K., Davvaz, B., Huang, S.: On derivations of prime and semi-prime Gamma rings. Boletim da Sociedade Paranaense de Matemática. 37(2), 157-166 (2019).
  • [7] Kyuno, S., Nobusawa, N., Smith, M. B.: Regular gamma rings. Tsukuba journal of mathematics. 11(2), 371-382 (1987).
  • [8] Estaji, A. A., Khorasani, A. S., Baghdari, S.: Multiplication Ideals in Gamma-rings. Journal of Hyperstructures. 2(1), (2013).
  • [9] Aydın, N., Demir, Ç., Karalarlıo˘glu Camcı, D.: The source of semiprimeness of rings. Communications of the Korean Mathematical Society. 33(4), 1083-1096 (2018).
  • [10] Arslan, O., Düzkaya, N.: The Source of Semi-Primeness of 􀀀-Rings. Fundamentals of Contemporary Mathematical Sciences. 4(2), 87-95 (2023).
  • [11] Karalarlıoglu Camcı, D.: Source of Semiprimeness and Multiplicative (generalized) Derivations in Rings. PhD dissertation. Çanakkale Onsekiz Mart University, Ç, (2017).
  • [12] Yeşil, D., Karalarlıoğlu Camcı, D.: The Source of Primeness of Rings. Journal of New Theory. 41, 100-104 (2022).
  • [13] Tabatabaee, Z. S., Roodbarylor, T.: The Construction of Fraction Gamma Rings and Local Gamma Rings by Using Commutative Gamma Rings. Journal of Mathematical Extension. 12(1), 73-86 (2018).
  • [14] Dükel, K. Ç., Çeven, Y.: Additivity of Multiplicative Isomorphisms in Gamma Rings. Palestine Journal of Mathematics. 6, (2017).
  • [15] Paul, R.: On various types of ideals of 􀀀-rings and the corresponding operator rings. International Journal of engineering Research and Applications. 5(8), 95-98 (2015).
  • [16] Adham Abdallah, Q.: Derivations on 􀀀-Rings, Prime 􀀀-Rings and Semiprime 􀀀-Rings. Doctoral Thesis. Faculty of Graduate Studies, Hebron University, Hebron, Palestine. (2017).
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematiksel Yöntemler ve Özel Fonksiyonlar
Bölüm Articles
Yazarlar

Didem Yeşil 0000-0003-0666-9410

Rasie Mekera 0000-0002-0092-2991

Erken Görünüm Tarihi 21 Ocak 2024
Yayımlanma Tarihi 28 Ocak 2024
Gönderilme Tarihi 12 Kasım 2023
Kabul Tarihi 2 Ocak 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 12 Sayı: 1

Kaynak Göster

APA Yeşil, D., & Mekera, R. (2024). The Source of $\Gamma$-Primeness on $\Gamma$-Rings. Mathematical Sciences and Applications E-Notes, 12(1), 36-42. https://doi.org/10.36753/mathenot.1389757
AMA Yeşil D, Mekera R. The Source of $\Gamma$-Primeness on $\Gamma$-Rings. Math. Sci. Appl. E-Notes. Ocak 2024;12(1):36-42. doi:10.36753/mathenot.1389757
Chicago Yeşil, Didem, ve Rasie Mekera. “The Source of $\Gamma$-Primeness on $\Gamma$-Rings”. Mathematical Sciences and Applications E-Notes 12, sy. 1 (Ocak 2024): 36-42. https://doi.org/10.36753/mathenot.1389757.
EndNote Yeşil D, Mekera R (01 Ocak 2024) The Source of $\Gamma$-Primeness on $\Gamma$-Rings. Mathematical Sciences and Applications E-Notes 12 1 36–42.
IEEE D. Yeşil ve R. Mekera, “The Source of $\Gamma$-Primeness on $\Gamma$-Rings”, Math. Sci. Appl. E-Notes, c. 12, sy. 1, ss. 36–42, 2024, doi: 10.36753/mathenot.1389757.
ISNAD Yeşil, Didem - Mekera, Rasie. “The Source of $\Gamma$-Primeness on $\Gamma$-Rings”. Mathematical Sciences and Applications E-Notes 12/1 (Ocak 2024), 36-42. https://doi.org/10.36753/mathenot.1389757.
JAMA Yeşil D, Mekera R. The Source of $\Gamma$-Primeness on $\Gamma$-Rings. Math. Sci. Appl. E-Notes. 2024;12:36–42.
MLA Yeşil, Didem ve Rasie Mekera. “The Source of $\Gamma$-Primeness on $\Gamma$-Rings”. Mathematical Sciences and Applications E-Notes, c. 12, sy. 1, 2024, ss. 36-42, doi:10.36753/mathenot.1389757.
Vancouver Yeşil D, Mekera R. The Source of $\Gamma$-Primeness on $\Gamma$-Rings. Math. Sci. Appl. E-Notes. 2024;12(1):36-42.
 Kapak Resmi İndir

20477

The published articles in MSAEN are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.