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Year 2021, Volume: 42 Issue: 1, 115 - 122, 29.03.2021

Emin Aygun , Betül Erdal

https://doi.org/10.17776/csj.738926

Abstract

References

  • [1] Molodtsov D., Soft Set Theory First Results, Comput. Math. Appl., 37 (1999) 19–31.
  • [2] Maji P.K., Biswas R., Roy, R., An Application of Soft Sets in A Decision-Making Problem, Comput. Math. Appl., 44 (2002) 1077–1083.
  • [3] Maji P.K., Biswas R., Roy R., Soft Set Theory, Comput. Math. Appl., 45 (2003) 555–562.
  • [4] Feng F., Li Y., Fotea V.L., Application of Level Soft Sets in Decision Making Based on İnterval-Valued Fuzzy Soft Sets, Comput. Math. Appl., 60 (2010) 1756-1767.
  • [5] Feng F., Li Y., Cagman N. Generalized Uni–İnt Decision Making Schemes Based on Choice Value Soft Sets, Eur. J. Oper. Res., 220 (2012) 162–170.
  • [6] Cagman N., Enginoglu S., Soft Set Theory and Uni–İnt Decision Making, Eur. J. Oper. Res., 207 (2010) 848–855.
  • [7] Aygun E., Soft Matrix Product and Soft Cryptosystem, Filomat, 32:19 (2018) 6519–6530.
  • [8] Aygun E., Kamacı H., Some Generalized Operations in Soft Set Theory and Their Role in Similarity and Decision Making, J. Intell. Fuzzy Syst., 36 (2019) 6537–6547.
  • [9] Aktas H., Cagman N., Soft Sets and Soft Groups, Inform. Sci., 177 (2007) 2726-2735.
  • [10] Feng F., Jun Y.B., Zhao X.Z. Soft Semirings, Comput. Math. Appl., 56 (2008) 2621–2628.
  • [11] Acar U., Koyuncu F., Tanay B., Soft Sets and Soft Rings, Comput. Math. Appl., 59 (2010) 3458-3463.
  • [12] Ali M.I., Shabir M., Shum K.P., On Soft Ideals over Semigroups. Southeast Asian Bull. Math., 34 (2010) 595-610.
  • [13] Atagun A.O., Sezgin A., Soft Substructures of Rings, fields and modules, Comput. Math. Appl 61 (3) (2011) 592-601.
  • [14] Sezgin A., Atagun A.O., Aygun E., A Note on Soft Near-Rings and Idealistic Soft Near-Rings, Filomat 25 (1) (2011) 53- 68.
  • [15] Sezgin A., Atagun A.O. Soft Groups and Normalistic Soft Groups, Comput. Math. Appl, 62 (2) (2011) 1457-1467.
  • [16] Atagun A.O., Aygun E., Groups of Soft Sets., J. Intell. Fuzzy Syst., 30 (2016) 729-733.
  • [17] Song S.Z., Kim H.S., Jun Y.B., Ideal Theory in Semigroups Based on Intersectional Soft Sets, Sci. World J., (2014) 136424.
  • [18] Sezgin A., Cagman N., Atagun A.O., Ali M.I., Turkmen E., Soft Intersection Semigroups, Ideals and Bi-Ideals: a New Application on Semigroup Theory I. Filomat, 29(5) (2015) 917-946.
  • [19] Sezgin A., Cagman N., Atagun A.O., Soft Intersection Interior Ideals, Quasi-ideals and Generalized Bi-Ideals: A New Approach to Semigroup Theory II., J. Multi. Valued Log.S, 3.1-2(2014) 161-207.
  • [20] Atıyah M., Macdonald I.G. Introduction to Commutative Algebra, Addison Wesley, (1994).
  • [21] Howie J.M., An Introduction to Semigroup Theory, Academic Press, (1976).

Radicals of soft intersectıonal ideals in semigroups

Year 2021, Volume: 42 Issue: 1, 115 - 122, 29.03.2021

Emin Aygun , Betül Erdal

https://doi.org/10.17776/csj.738926

Abstract

In this paper, we introduce IS-radical, IS-quasi radical, IS-interior radical and IS-nil radical in semigroups. We obtain radical structures that will contribute to the theoretical studies of soft sets. We consider the ideal structures of intersectional soft sets in semigroups and we define IS-radical, IS-quasi radical, IS-interior radical and IS-nil radical. We use two different methods to define the soft radicals and give the results. In our study, we also give several examples and propositions to see differences among these structures.

Keywords

Soft radical IS-radical IS-quasi radical IS-interior radical IS-nil radical

References

  • [1] Molodtsov D., Soft Set Theory First Results, Comput. Math. Appl., 37 (1999) 19–31.
  • [2] Maji P.K., Biswas R., Roy, R., An Application of Soft Sets in A Decision-Making Problem, Comput. Math. Appl., 44 (2002) 1077–1083.
  • [3] Maji P.K., Biswas R., Roy R., Soft Set Theory, Comput. Math. Appl., 45 (2003) 555–562.
  • [4] Feng F., Li Y., Fotea V.L., Application of Level Soft Sets in Decision Making Based on İnterval-Valued Fuzzy Soft Sets, Comput. Math. Appl., 60 (2010) 1756-1767.
  • [5] Feng F., Li Y., Cagman N. Generalized Uni–İnt Decision Making Schemes Based on Choice Value Soft Sets, Eur. J. Oper. Res., 220 (2012) 162–170.
  • [6] Cagman N., Enginoglu S., Soft Set Theory and Uni–İnt Decision Making, Eur. J. Oper. Res., 207 (2010) 848–855.
  • [7] Aygun E., Soft Matrix Product and Soft Cryptosystem, Filomat, 32:19 (2018) 6519–6530.
  • [8] Aygun E., Kamacı H., Some Generalized Operations in Soft Set Theory and Their Role in Similarity and Decision Making, J. Intell. Fuzzy Syst., 36 (2019) 6537–6547.
  • [9] Aktas H., Cagman N., Soft Sets and Soft Groups, Inform. Sci., 177 (2007) 2726-2735.
  • [10] Feng F., Jun Y.B., Zhao X.Z. Soft Semirings, Comput. Math. Appl., 56 (2008) 2621–2628.
  • [11] Acar U., Koyuncu F., Tanay B., Soft Sets and Soft Rings, Comput. Math. Appl., 59 (2010) 3458-3463.
  • [12] Ali M.I., Shabir M., Shum K.P., On Soft Ideals over Semigroups. Southeast Asian Bull. Math., 34 (2010) 595-610.
  • [13] Atagun A.O., Sezgin A., Soft Substructures of Rings, fields and modules, Comput. Math. Appl 61 (3) (2011) 592-601.
  • [14] Sezgin A., Atagun A.O., Aygun E., A Note on Soft Near-Rings and Idealistic Soft Near-Rings, Filomat 25 (1) (2011) 53- 68.
  • [15] Sezgin A., Atagun A.O. Soft Groups and Normalistic Soft Groups, Comput. Math. Appl, 62 (2) (2011) 1457-1467.
  • [16] Atagun A.O., Aygun E., Groups of Soft Sets., J. Intell. Fuzzy Syst., 30 (2016) 729-733.
  • [17] Song S.Z., Kim H.S., Jun Y.B., Ideal Theory in Semigroups Based on Intersectional Soft Sets, Sci. World J., (2014) 136424.
  • [18] Sezgin A., Cagman N., Atagun A.O., Ali M.I., Turkmen E., Soft Intersection Semigroups, Ideals and Bi-Ideals: a New Application on Semigroup Theory I. Filomat, 29(5) (2015) 917-946.
  • [19] Sezgin A., Cagman N., Atagun A.O., Soft Intersection Interior Ideals, Quasi-ideals and Generalized Bi-Ideals: A New Approach to Semigroup Theory II., J. Multi. Valued Log.S, 3.1-2(2014) 161-207.
  • [20] Atıyah M., Macdonald I.G. Introduction to Commutative Algebra, Addison Wesley, (1994).
  • [21] Howie J.M., An Introduction to Semigroup Theory, Academic Press, (1976).
There are 21 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Natural Sciences
Authors

Emin Aygun 0000-0003-3503-0552

Betül Erdal 0000-0002-1266-7940

Publication Date March 29, 2021
Submission Date May 17, 2020
Acceptance Date January 25, 2021
Published in Issue Year 2021Volume: 42 Issue: 1

Cite

APA Aygun, E., & Erdal, B. (2021). Radicals of soft intersectıonal ideals in semigroups. Cumhuriyet Science Journal, 42(1), 115-122. https://doi.org/10.17776/csj.738926