Research Article

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

Volume: 12 Number: 1 January 28, 2024
EN

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

Abstract

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.

Keywords

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

References

  1. [1] Nobusawa, N.: On a generalization of the ring theory. Osaka Journal of Mathematics. 1, 81-89 (1964).
  2. [2] Barnes,W.: On the 􀀀-rings of Nobusawa. Pacific Journal of Mathematics. 18(3), 411-422 (1966).
  3. [3] Kyuno, S.: On prime 􀀀-rings. Pacific Journal of Mathematics. 75(1), 185-190 (1978).
  4. [4] Kyuno, S.: Prime ideals in 􀀀-rings. Pacific Journal of Mathematics. 98(2), 375-379 (1982).
  5. [5] Ravisankar, T. S., Shukla, U. S.: Structure of 􀀀-rings. Pacific Journal of Mathematics. 82(2), 537-559 (1979).
  6. [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. [7] Kyuno, S., Nobusawa, N., Smith, M. B.: Regular gamma rings. Tsukuba journal of mathematics. 11(2), 371-382 (1987).
  8. [8] Estaji, A. A., Khorasani, A. S., Baghdari, S.: Multiplication Ideals in Gamma-rings. Journal of Hyperstructures. 2(1), (2013).
  9. [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. [10] Arslan, O., Düzkaya, N.: The Source of Semi-Primeness of 􀀀-Rings. Fundamentals of Contemporary Mathematical Sciences. 4(2), 87-95 (2023).
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
1.Yeşil D, Mekera R. The Source of $\Gamma$-Primeness on $\Gamma$-Rings. Math. Sci. Appl. E-Notes. 2024;12(1):36-42. doi:10.36753/mathenot.1389757
Chicago
Yeşil, Didem, and Rasie Mekera. 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.
EndNote
Yeşil D, Mekera R (January 1, 2024) The Source of $\Gamma$-Primeness on $\Gamma$-Rings. Mathematical Sciences and Applications E-Notes 12 1 36–42.
IEEE
[1]D. Yeşil and R. Mekera, “The Source of $\Gamma$-Primeness on $\Gamma$-Rings”, Math. Sci. Appl. E-Notes, vol. 12, no. 1, pp. 36–42, Jan. 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 (January 1, 2024): 36-42. https://doi.org/10.36753/mathenot.1389757.
JAMA
1.Yeşil D, Mekera R. The Source of $\Gamma$-Primeness on $\Gamma$-Rings. Math. Sci. Appl. E-Notes. 2024;12:36–42.
MLA
Yeşil, Didem, and Rasie Mekera. “The Source of $\Gamma$-Primeness on $\Gamma$-Rings”. Mathematical Sciences and Applications E-Notes, vol. 12, no. 1, Jan. 2024, pp. 36-42, doi:10.36753/mathenot.1389757.
Vancouver
1.Didem Yeşil, Rasie Mekera. The Source of $\Gamma$-Primeness on $\Gamma$-Rings. Math. Sci. Appl. E-Notes. 2024 Jan. 1;12(1):36-42. doi:10.36753/mathenot.1389757