On the structure and applications of neutrosophic prime ideals

Ali Yahya Hummdi; Amr Elrawy; Ali Yahya Hummdi; Amr Elrawy

doi:10.3934/math.2025743

AIMS Mathematics

2025, Volume 10, Issue 7: 16597-16610. doi: 10.3934/math.2025743

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Research article

On the structure and applications of neutrosophic prime ideals

Ali Yahya Hummdi ^{1
,
,},
Amr Elrawy ²

1.
Department of Mathematics, College of Science, King Khalid University, Abha 61471, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, South Valley University, Qena 83523, Egypt

Received: 13 May 2025 Revised: 03 July 2025 Accepted: 09 July 2025 Published: 23 July 2025
MSC : 46J20, 08A72, 13A15, 11R44

This study explores key characteristics associated with neutrosophic prime ideals. In particular, it is shown that the image corresponding to these ideals contains exactly two different elements. The work also extends the concept of classical prime ideals by incorporating neutrosophic logic. A new approach to identifying prime ideals using neutrosophic points is introduced. Furthermore, the paper compares various definitions of neutrosophic prime ideals and examines the connections between them. Finally, an application is used to illustrate the role of neutrosophic prime ideals in decision-making processes.
- neutrosophic set,
- neutrosophic prime ideal,
- ideal
Citation: Ali Yahya Hummdi, Amr Elrawy. On the structure and applications of neutrosophic prime ideals[J]. AIMS Mathematics, 2025, 10(7): 16597-16610. doi: 10.3934/math.2025743

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Abstract

This study explores key characteristics associated with neutrosophic prime ideals. In particular, it is shown that the image corresponding to these ideals contains exactly two different elements. The work also extends the concept of classical prime ideals by incorporating neutrosophic logic. A new approach to identifying prime ideals using neutrosophic points is introduced. Furthermore, the paper compares various definitions of neutrosophic prime ideals and examines the connections between them. Finally, an application is used to illustrate the role of neutrosophic prime ideals in decision-making processes.

References

[1]	K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Set. Syst., 20 (1986), 87–96. https://doi.org/10.1016/S0165-0114(86)80034-3 doi: 10.1016/S0165-0114(86)80034-3
[2]	V. Çetkin, H. Ayg$\ddot{u}$n, An approach to neutrosophic subgroup and its fundamental properties, J. Intell. Fuzzy Syst., 29 (2015), 1941–1947.
[3]	V. Çetkin, H. Ayg$\ddot{u}$n, An approach to neutrosophic ideals, Univer. J. Math. Appl., 1 (2018), 132–136.
[4]	V. Çetkin, H. Ayg$\ddot{u}$n, An approach to neutrosophic subrings, Sakarya Univer. J. Sci., 23 (2019), 472–477.
[5]	A. Elrawy, M. Abdalla, M. A. Saleem, Some results on neutrosophic group, J. Math., 2023 (2023). http://dx.doi.org/10.1155/2023/4540367 doi: 10.1155/2023/4540367
[6]	A. Elrawy, M. Abdalla, Results on a neutrosophic sub-rings, AIMS Math., 8 (2023), 21393–21405. http://dx.doi.org/10.3934/math.20231090 doi: 10.3934/math.20231090
[7]	A. Y. Elrawy, A. Hummdi, On neutrosophic ideals and prime ideals in rings, AIMS Math., 9 (2024), 24762–24775. http://dx.doi.org/10.3934/math.20241205 doi: 10.3934/math.20241205
[8]	A. Y. Hummdi, A. Elrawy, A. A. Temraz, Neutrosophic modules over modules, AIMS Math., 9 (2024), 35964–35977. http://dx.doi.org/10.3934/math.20241705 doi: 10.3934/math.20241705
[9]	N. Olgun, M. Bal, Neutrosophic modules, Neutrosophic Oper. Res., 2 (2017), 181–192.
[10]	F. Smarandache, Neutrosophy, Neutrosophic probability, American Research Press, 1998.
[11]	F. Smarandache, Neutrosophic set-a generalization of the intuitionistic fuzzy set, Int. J. Pure Appl. Math., 24 (2005), 287.
[12]	F. Smarandache, Neutrosophic set-a generalization of the intuitionistic fuzzy set, J. Defen. Res. Manag., 1 (2010), 107–116.
[13]	F. Smarandache, Neutrosophic perspectives: Triplets, duplets, multisets, hybrid operators, modal logic, hedge algebras and applications, Bruxelles: Pons Editions, 2017.
[14]	H. B. Wang, F. Smarandache, Y. Q. Zhang, R. Sunderraman, Single valued neutrosophic sets, Infinite study, 2010,410–413.
[15]	L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X doi: 10.1016/S0019-9958(65)90241-X
[16]	X. H. Zhang, C. X. B, F. Smarandache, J. H. Dai, New inclusion relation of neutrosophic sets with applications and related lattice structure, Int. J. Mach. Learn. Cyber., 9 (2018), 1753–1763. https://doi.org/10.1007/s13042-018-0817-6 doi: 10.1007/s13042-018-0817-6

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