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Journals / Fundamentals of Contemporary Mathematical Sciences / 2026 / Volume: 7 Issue: 2

Soft N-Clogroups over Near-Rings and Their Extended Operations

İncinur Yılmaz(ERCIYES UNIVERSITY, FACULTY OF SCIENCE)0000-0001-6481-8918
Emin Aygun(ERCIYES UNIVERSITY, FACULTY OF SCIENCE)0000-0003-3503-0552
Pages
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Publication Date
2026-07-31
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⚡ TL;DR(Too Long; Didn't Read)

Moreover, we examine the behavior of soft N -clogroups under near-ring homomorphisms and show that preimages preserve the soft N -clogroup structure, whereas homomorphic images do not necessarily preserve it.

📌 3 Key Takeaways

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Objective & Hypothesis:In this paper, we introduce the notion of a soft N -clogroup over a near-ring by combining the classical concept of N -clogroups with soft set theory.
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Key Findings & Data:This framework provides a parameter-dependent extension of the subgroup-generation mechanism induced by multiplicative action in near-rings.
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Conclusion & Impact:Moreover, we examine the behavior of soft N -clogroups under near-ring homomorphisms and show that preimages preserve the soft N -clogroup structure, whereas homomorphic images do not necessarily preserve it.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Near-rings · Soft Sets · n-clogroups

Abstract

In this paper, we introduce the notion of a soft N -clogroup over a near-ring by combining the classical concept of N -clogroups with soft set theory. This framework provides a parameter-dependent extension of the subgroup-generation mechanism induced by multiplicative action in near-rings. We define soft N -clogroups and soft sub-N -clogroups and present illustrative examples clarifying their structural behavior. We further investigate the behavior of these structures under extended union and extended intersection operations. The associativity of these extended operations is established within the soft N - clogroup framework. The obtained results provide a systematic structural analysis of soft N -clogroups and clarify the behavior of extended operations in this setting. Moreover, we examine the behavior of soft N -clogroups under near-ring homomorphisms and show that preimages preserve the soft N -clogroup structure, whereas homomorphic images do not necessarily preserve it.

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Cite This Article

Yılmaz, İ., Aygun, E. (2026). Soft N-Clogroups over Near-Rings and Their Extended Operations. Fundamentals of Contemporary Mathematical Sciences, Volume: 7 Issue: 2. https://doi.org/10.54974/fcmathsci.1914514

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References (22)

  1. Acar U., Koyuncu F., Tanay B., Soft sets and soft rings, Computers & Mathematics with Applications, 59(11), 3458-3463, 2010.
  2. Aktaş H., Çağman N., Soft sets and soft groups, Information Sciences, 177(13), 2726-2735, 2007.
  3. Ali M.I., Feng F., Liu X., Min W.K., Shabir M., On some new operations in soft set theory, Computers & Mathematics with Applications, 57(9), 1547-1553, 2009.
  4. Atagün A.O., Sezgin A., Soft subnear-rings, soft ideals and soft N-subgroups of near-rings, Mathematical Sciences Letters, 7(1), 37–42, 2018.
  5. Aygün E., On the N-clogroups and v-prime Ideals in Near-rings, Ph.D. Thesis, Erciyes University, Kayseri, Türkiye, 2006.
  6. Aygün E., Kamacı H., Some new algebraic structures of soft sets, Soft Computing, 25(13), 8609-8626, 2021.
  7. Aygün E., Kamacı H., Two different types of soft near-fields, Punjab University Journal of Mathematics, 54(7), 429-440, 2022.
  8. Feng F., Jun Y.B., Zhao X., Soft semirings, Computers & Mathematics with Applications, 56(10), 2621-2628, 2008.
  9. Jun Y.B., Soft BCK/BCI-algebras, Computers & Mathematics with Applications, 56(5), 1408-1413, 2008.
  10. Jun Y.B., Park C.H., Applications of soft sets in ideal theory of BCK/BCI-algebras, Information Sciences, 178(11), 2466-2475, 2008.
  11. Maji P.K., Roy A.R., Biswas R., An application of soft sets in a decision making problem, Computers & Mathematics with Applications, 44(8-9), 1077-1083, 2002.
  12. Maji P.K., Biswas R., Roy A.R., Soft set theory, Computers & Mathematics with Applications, 45(4-5), 555-562, 2003.
  13. Molodtsov D.A., Soft set theory-first results, Computers & Mathematics with Applications, 37(4-5), 19-31, 1999.
  14. Molodtsov D.A., The Theory of Soft Sets (in Russian), URSS Publishers, Moscow, Russia, 2004.
  15. Molodtsov D.A., Leonov V.Y., Kovkov D.V., Soft sets technique and its application, Nechetkie Sistemy I Myagkie Vychisleniya, 1(1), 8-39, 2006.
  16. Park C.H., Jun Y.B., Öztürk M.A., Soft WS-algebras, Communications of the Korean Mathematical Society, 23(3), 313-324, 2008.
  17. Pawlak Z., Rough sets, International Journal of Computer and Information Sciences, 11(5), 341-356, 1982.
  18. Pei D., Miao D., From soft sets to information systems, Proceedings of the 2005 IEEE International Conference on Granular Computing, 2, 617-621, 2005.
  19. Sezgin A., Atagün A.O., Aygün E., A note on soft near-rings and idealistic soft near-rings, Filomat, 25(1), 53-68, 2011.
  20. Sezgin A., Atagün A.O., On operations of soft sets, Computers & Mathematics with Applications, 61(5), 1457-1467, 2011.
  21. Sun Q.-M., Zhang Z.-L., Liu J., Soft sets and soft modules, Rough Sets and Knowledge Technology, Lecture Notes in Computer Science, 5009, 403-409, 2008.
  22. Xiao Z., Chen L., Zhong B., Ye S., Recognition for soft information based on the theory of soft sets, Proceedings of the 2005 International Conference on Services Systems and Services Management (ICSSSM 2005), 2, 1104-1106, 2005.