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

Year 2024, Volume: 12 Issue: 1, 36 - 42, 28.01.2024

Didem Yeşil , Rasie Mekera

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

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] 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).