Research Article
Year 2021,
, 333 - 338, 30.06.2021
Abstract
This article introduces quasi-ideals in semirings on weak nearness approximation spaces. Concepts and definitions are given to clarify the subject of quasi ideals in semirings on weak nearness approximation spaces. Some basic properties of quasi ideals are also given. Furthermore, it is given that the definition of upper-near quasi ideals. And, it is examined that the relationship between quasi ideals and upper near quasi ideals. Therefore, the features described in this study will contribute greatly to the theoretical development of the nearness semirings theory.
References
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- [3] Peters J. F., Near sets, Special theory about nearness of objects, Fund. Inform., 75 (1-4) (2007) 407–433.
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- [6] İnan E., Öztürk M. A., Erratum and notes for near groups on nearness approximation spaces, Hacet. J. Math. Stat., 43 (2) (2014) 279-281.
- [7] İnan E., Öztürk M. A., Nearness rings, Ann. Fuzzy Math. Inform., 17(2) (2019) 115-132.
- [8] Öztürk M. A., Bekmezci İ. H., Gamma nearness semirings, Southeast sian Bull. Math., 44(4) (2020) 567-586.
- [9] Öztürk M. A., Jun Y. B., İz A., Gamma semigroups on weak nearness approximation spaces, J. Int. Math. Virtual Inst., 9(1) (2019) 53-72.
- [10] Öztürk M. A., Prime ideals of gamma semigroups on weak nearness approximation spaces, Asian-Eur. J. Math., 12 (2019).
- [11] Öztürk M. A., Bekmezci İ. H., Gamma nearness semirings, Southeast Asian Bull. Math., 44(4) (2020) 567-586.
- [12] Öztürk, M. A., and Temur, İ., Prime ideals of nearness semirings, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68(2) (2019) 1867-1878.
- [13] Öztürk M. A., Semiring on weak nearness approximation spaces, Ann. Fuzzy Math. Inform., 15(3) (2018) 227-241.
- [14] Vandier H. S., Note on a simple type of algebra in which cancellation law of addition does not hold, Bull. Am. Math. Soc., 40(12) (1934) 914-920.
- [15] Shabir A. M, Ali A., Batol S., A note on quasi ideal in semirings, Southeast Asian Bull. Math., 27 (5) (2004) 923-928.
- [16] Steinfeld, O, Quasi-Ideals in Rings and Semigroups, Akad´emiai Kiad´o, Budapest (1978).
- [17] Iseki K., Quasi-ideals in semirings without zero, Proc. Japan Acad., 34 (1958) 79-81.
- [18] Rao M. M. K., A study of quasi-interior ideals of semirings, Bull. Int. Math. Virtual Inst., 9(1) (2019) 287-300.
- [19] Rao M. M. K., Bi-quasi ideals and fuzzy bi-quasi ideals of Γ-semirings, Bull. Int. Math. Virtual Inst., 8(1) (2018) 45-53.
- [20] El-Madhoun N. R., Quasi ideals and bi-ideals on semigroups and semirings, MSc Thesis, The Islamic University of Gaza, Faculty of Science, 2007.
- [21] Golan J. S., Semirings and Their Applications, Kluwer Academic Publishers, 1999.
Year 2021,
, 333 - 338, 30.06.2021
Abstract
References
- [1] Pawlak Z., Rough sets, Int. J. Comput. Inform. Sci., 11 (5) (1982) 341–356.
- [2] Peters J. F., Near sets, General theory about nearness of objects, Appl. Math. Sci., 1 (53-56) (2007) 2609–2629.
- [3] Peters J. F., Near sets, Special theory about nearness of objects, Fund. Inform., 75 (1-4) (2007) 407–433.
- [4] Peters J. F., Near sets: An introduction, Math. Comput. Sci., 7 (1) (2013) 3–9.
- [5] İnan E., Öztürk M. A., Near groups on nearness approximation spaces, Hacet. J. Math. Stat., 41 (4) (2012) 545-558.
- [6] İnan E., Öztürk M. A., Erratum and notes for near groups on nearness approximation spaces, Hacet. J. Math. Stat., 43 (2) (2014) 279-281.
- [7] İnan E., Öztürk M. A., Nearness rings, Ann. Fuzzy Math. Inform., 17(2) (2019) 115-132.
- [8] Öztürk M. A., Bekmezci İ. H., Gamma nearness semirings, Southeast sian Bull. Math., 44(4) (2020) 567-586.
- [9] Öztürk M. A., Jun Y. B., İz A., Gamma semigroups on weak nearness approximation spaces, J. Int. Math. Virtual Inst., 9(1) (2019) 53-72.
- [10] Öztürk M. A., Prime ideals of gamma semigroups on weak nearness approximation spaces, Asian-Eur. J. Math., 12 (2019).
- [11] Öztürk M. A., Bekmezci İ. H., Gamma nearness semirings, Southeast Asian Bull. Math., 44(4) (2020) 567-586.
- [12] Öztürk, M. A., and Temur, İ., Prime ideals of nearness semirings, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68(2) (2019) 1867-1878.
- [13] Öztürk M. A., Semiring on weak nearness approximation spaces, Ann. Fuzzy Math. Inform., 15(3) (2018) 227-241.
- [14] Vandier H. S., Note on a simple type of algebra in which cancellation law of addition does not hold, Bull. Am. Math. Soc., 40(12) (1934) 914-920.
- [15] Shabir A. M, Ali A., Batol S., A note on quasi ideal in semirings, Southeast Asian Bull. Math., 27 (5) (2004) 923-928.
- [16] Steinfeld, O, Quasi-Ideals in Rings and Semigroups, Akad´emiai Kiad´o, Budapest (1978).
- [17] Iseki K., Quasi-ideals in semirings without zero, Proc. Japan Acad., 34 (1958) 79-81.
- [18] Rao M. M. K., A study of quasi-interior ideals of semirings, Bull. Int. Math. Virtual Inst., 9(1) (2019) 287-300.
- [19] Rao M. M. K., Bi-quasi ideals and fuzzy bi-quasi ideals of Γ-semirings, Bull. Int. Math. Virtual Inst., 8(1) (2018) 45-53.
- [20] El-Madhoun N. R., Quasi ideals and bi-ideals on semigroups and semirings, MSc Thesis, The Islamic University of Gaza, Faculty of Science, 2007.
- [21] Golan J. S., Semirings and Their Applications, Kluwer Academic Publishers, 1999.
There are 21 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Natural Sciences |
| Authors | |
| Publication Date | June 30, 2021 |
| Submission Date | January 22, 2021 |
| Acceptance Date | May 4, 2021 |
| Published in Issue | Year 2021 |