Extensions of soft fractional Ideals using soft semistar operations approach on Integral domains

Document Type : Research Paper

Authors

Department of Mathematics, Faculty of Sciences, Jamia Millia Islamia, New Delhi, India

Abstract

A comprehensive mathematical technique for handling uncertainty is the Molodtsov introduced idea of soft sets. In this paper, the operations leading to themselves from the set of undeniable soft fractional ideals are instigated. We provide some extensions of soft fractional ideals using the notion of overrings. We bring out the notion of soft semistar operations in relation to undeniable soft fractional ideals and connect it to the current notions of star and semistar operations. We also demonstrate the formation of complete soft lattice from the collection of all soft semistar operations on integral domains.

Keywords

References

[1] U. Acar, F. Koyuncu, and B. Tanay, Soft sets and soft rings, Computers & Mathematics with Applications, (11) 59 (2010), 3458-3463.
[2] O. Akira and M. Ryûki, Semistar-operations on integral domains, Mathematics Journal of Toyama University, 17 (1994), 1-21.
[3] H. Aktaş and N. Çağman, Soft sets and soft groups, Information Sciences, (13) 177 (2007), 2726-2735.
[4] D. D. Anderson and D. F. Anderson, Examples of star operations on integral domains, Communications in Algebra, (5) 18 (1990), 1621-1643.
[5] A. O. Atagün and A. Sezgin, Soft substructures of rings, fields and modules, Computers & Mathematics with Applications, (3) 61 (2011), 592-601.
[6] R. Gilmer, Multiplicative ideal theory, Queen’s Papers in Pure and Applied Mathematics, 90, 1992 (Corrected reprint of the 1972 edition).
[7] R. Gilmer and J. Ohm, Integral domains with quotient overrings, Mathematische Annalen, (2) 153 (1964), 97-103.
[8] Y. B. Jun, Soft bck/bci-algebras, Computers & Mathematics with Applications, (5) 56 (2008), 1408-1413.
[9] Y. B. Jun and C. H. Park, Applications of soft sets in ideal theory of bck/bci-algebras, Information Sciences, (11) 178 (2008), 2466-2475.
[10] F. Karaaslan, N. Çağman, and S. Enginoglu, Soft lattices, Journal of New Results in Science, (1) 1 (2012), 5-17.
[11] P. K. Maji, R. Biswas, and A. R. Roy, Soft set theory, Computers & Mathematics with Applications, (4-5) 45 (2003), 555-562.
[12] D. Molodtsov, Soft set theory–first results, Computers & Mathematics with Applications, (4-5) 37 (1999), 19-31.
[13] G. Picozza, Semistar operations and multiplicative ideal theory, PhD thesis, Universita Degli Studi “Roma Tre”, 2004.
[14] G. Picozza, Star operations on overrings and semistar operations, Communications in Algebra, (6) 33 (2005), 2051-2073.
[15] M. Ryûki and S. Takasi, Semistar-operations on integral domains II, Mathematics Journal of Toyama University, 18 (1995), 155-161.
[16] Q. M. Sun, Z. L. Zhang, and J. Liu, Soft sets and soft modules, Lecture Notes in Computer Science, 5009 (2008), 403-409.
[17] A. Taouti and W. A. Khan, A note on some new soft structures, Journal of Mathematical and Computational Sciences, (3) 4 (2014), 522-530.
[18] A. Taouti, W. A. Khan, and S. Karkain Note on soft fractional ideal of ring, Journal of Mathematical and Computational Sciences, (5) 8 (2018), 579-583.
[19] E. Türkmen and A. Pancar, On some new operations in soft module theory, Neural Computing and Applications, (6) 22 (2013), 1233-1237.
Journal of Algebra and Related Topics
Volume 13, Issue 2
December 2025
Pages 137-148

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