Yakınlık Yarı Halkalarının Bi İdealleri

Öz

Bi idealler, quasi ideallerin bir genelleştirmesidir. Bu çalışmada, zayıf yakınlık yaklaşım uzaylarında bi-idealler kavramı tanımlandı. Daha sonra, konuyla ilgili bazı tanımlar ve kavramlar açıklandı. Ayrıca, yakınlık m-bi idealleri ve yakınlık (m,n)-quasi ideallerinin tanımları verildi. Böylece, yakınlık m-bi idealleri ve yakınlık (m,n)-quasi ideallerinin aralarındaki ilişkiyi inceledik.

Anahtar Kelimeler

• Yakınlık Yaklaşım Uzayları
• Yarı Halkalar
• Yakınlık Yarı Halkaları
• Quasi idealler
• Bi idealler.

Bi Ideals of Nearness Semirings

Öz

Bi ideals are the generalisation of quasi ideals. In this article, it is defined that the notion of bi-ideals in semirings on weak nearness approximation spaces. Afterwards, it is explained that some of the concepts and definitions related to the subject. Also, it is given that the definition of nearness m-bi ideals and nearness (m,n)-quasi ideals. Thus, we examine the relationship between nearness m-bi ideals and nearness (m,n)-quasi ideals .

Anahtar Kelimeler

• Nearness approximation space
• Semirings
• Nearness semiring
• Quasi ideals
• Bi ideals.

Kaynakça

1. Pawlak, Z. (1982). Rough sets, Int. J. Comput. Inform. Sci. 11(5), 341–356.
2. Peters, J. F. (2007). Near sets, General theory about nearness of objects, Appl. Math. Sci. 1 (53-56), 2609–2629.
3. Peters, J. F. (2007). Near sets, Special theory about nearness of objects, Fund. Inform. 75 (1-4), 407–433.
4. Peters, J. F. (2013). Near sets: An introduction, Math. Comput. Sci. 7 (1), 3–9.
5. İnan, E. and Öztürk, M. A. (2012). Near groups on nearness approximation spaces, Hacet. J. Math. Stat. 41 (4), 545-558.
6. Öztürk, M. A. (2018)Semiring on weak nearness approximation spaces, Ann. Fuzzy Math. Inform, 15(3), 227-241.
7. Öztürk, M. A. And Temur, İ. (2019). Prime ideals of nearness semirings, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 68(2),1867-1878.
8. Öztürk, M. A. and Bekmezci, İ.H. (2020). Gamma nearness semirings, Southeast Asian Bull. Math. 44(4), 567-586.

9. Vandier, H.S.(1934). Note on a simple type of algebra in which cancellation law of addition does not hold, Bull. Am. Math. Soc., 40(12),914-920.
10. Shabir, A. M and Batod, A. (2004). A note on quasi ideal in semirings, Southeast Asian Bull. Math., 27(5), 923-928.
11. Good, R.A. and Hughes, D.R.(1952). Associated groups for a semigroups, Bull. Am. Math. Soc., 58 (6), 624-625.
12. Lajos, S. and Szasz, F.A. (1970) On the bi-ideals in associative ring, Proc. Japan Acad., 46 (6), 505-507.
13. Tekin, Ö. (2021). Quasi Ideals of Nearness Semirings, Cumhuriyet Sci. J. 42(2), 333-338.
14. Öztürk, M. A., Jun, Y. B. and İz, A. (2019). Gamma semigroups on weak nearness approximation spaces, J. Int. Math. Virtual Inst. 9 (1), 53-72.
15. El-Madhoun, N. R. (2007). Quasi ideals and bi-ideals on semigroups and semirings, MSc Thesis, Department of Mathematics, Faculty of Science, The Islamic University of Gaza.
16. Golan, J. S. (1999). Semirings and Their Applications, Kluwer Academic Publishers.