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The Category of Soft Topological Hyperrings

Year 2021, Volume: 6 Issue: 1, 6 - 13, 30.04.2021

Abstract

In this study, which focuses on the intersection of soft set theory and topological hyperrings,
the concept of soft topological hyperrings is proposed and its relation with topological hyperrings is
examined. Morever, some characterizations related to the family of soft topological hyperrings are obtained
and the category of soft topological hypergrupoids is establshed. Finally, the concept of soft topological
subhyperrings is described and several structural features are studied.

References

  • [1] Marty, F. (1934). Sur une Generalisation de la Notion de Groupe. 8th Congress Mathematiciens Scandinaves, Stockholm, pp. 45–49.
  • [2] Molodtsov, D. A.(1999). Soft set theory-First results. Comput. Math. Appl., 37(4-5), 19–31.
  • [3] Maji, P. K., Biswas, R., Roy, A. R. (2003).Soft set theory, Comput. Math. Appl., 45(4-5), 555–562.
  • [4] Oguz, G., Icen, I., Gursoy, M.H.(2019). Actions of soft groups.Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68(1), 1163–1174.
  • [5] Aktas, H., Cagman, N.(2007). Soft sets and soft groups. Inform. Sci., 77(13), 2726–2735.
  • [6] Atagun A. O., Sezgin A. (2011). Soft substructures of rings, fields and modules, Comput. Math. Appl., 61, 592–601.
  • [7] Oguz, G., Gursoy, M.H., Icen, I.(2019). On soft topological categories. Hacet. J. Math. Stat., 48(6), 1675–1681.
  • [8] Shabir, M., Naz, M.(2011). On soft topological spaces. Comput. Math. Appl., 61(7), 1786–1799.
  • [9] Oguz, G. (2020). Soft Topological Transformation Groups. Mathematics, 8(9), 1545.
  • [10] Aygunoglu, A., Aygun, A.(2012). Some notes on soft topological spaces. Neural Comput. Appl., 22(1), 113–119.
  • [11] Oguz, G., Icen, I., Gursoy, M.H.(2020). A New Concept in the Soft Theory: Soft Groupoids. Southeast Asian Bull. Math., 44(4), 555–565.
  • [12] Yamak, S., Kazanci, O., Davvaz, B.(2011). Soft hyperstructure. Comput. Math. with Appl., 62(2), 797–803.
  • [13] Tasbozan H., Icen I., Bagrmaz, N. and Ozcan, A.F.(2017). Soft Sets and Soft Topology on Nearness Approximation Space, Filomat 31:13, 41174125.
  • [14] Oguz, G.(2020). A New View on Topological Polygroups. Turkish Journal of Science, 5(2), 110–117.
  • [15] Selvachandran, G., Salleh, A. R. (2013). Soft hypergroups and soft hypergroup homomorphism. In: AIP Conference Proceedings. American Institute of Physics, 1522(1), 821–827.
  • [16] Wang, J., Yin, M., Gu, W. (2011). Soft polygroups, Comput. Math. Appl., 62(9), 3529–3537.
  • [17] Selvachandran, G. (2015). Introduction to the theory of soft hyperrings and soft hyperring homomorphism. JP J. Algebra, Number Theory Appl., 36(3), 279–294.
  • [18] Shah, T., Shaheen, S. (2014). Soft topological groups and rings, Ann. Fuzzy Math. Inform., 7(5), 725–743.
  • [19] Davvaz, B., Leoreanu-Fotea, V. (2007). Hyperring theory and applications, International Academic Press, USA.
  • [20] Nodehi, M., Norouzi, M., Dehghan, O. R. (2020). An introduction to topological hyperrings. Casp. J. Math. Sci., 9(2), 210–223.
  • [21] Davvaz, B. (2004). Isomorphism theorems on hyperrings. Indian J. Pure Appl.Math., 35(3), 321–331.
  • [22] Velrajan, M., Asokkumar, A. (2010). Note on isomorphism theorems of hyperrings. Int. j. math. math. sci.,
  • [23] Maji,P.K., Roy, A.R., Biswas, R.(2002). An application of soft sets in a decision making problem, Comput. Math. Appl., 44, 1077–1083.
  • [24] Kazanci, O., Yilmaz, S., Yamak, S. (2010). Soft sets and soft BCH-algebras, Hacet. J. Math. Stat., 39, 205–217.
  • [25] Jinyan, W. A. N. G., Minghao, Y. . N., Wenxiang, G. U. (2015). Soft hyperrings and their (fuzzy) isomorphism theorems.Hacet. J. Math. Stat., 44(6), 1463–1475.
  • [26] Heidari,D. Davvaz,B. and Modarres, S. M. S. (2016). Topological polygroups, Bull. Malaysian Math. Sci. Soc., 39(2), 707-721.
Year 2021, Volume: 6 Issue: 1, 6 - 13, 30.04.2021

Abstract

References

  • [1] Marty, F. (1934). Sur une Generalisation de la Notion de Groupe. 8th Congress Mathematiciens Scandinaves, Stockholm, pp. 45–49.
  • [2] Molodtsov, D. A.(1999). Soft set theory-First results. Comput. Math. Appl., 37(4-5), 19–31.
  • [3] Maji, P. K., Biswas, R., Roy, A. R. (2003).Soft set theory, Comput. Math. Appl., 45(4-5), 555–562.
  • [4] Oguz, G., Icen, I., Gursoy, M.H.(2019). Actions of soft groups.Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68(1), 1163–1174.
  • [5] Aktas, H., Cagman, N.(2007). Soft sets and soft groups. Inform. Sci., 77(13), 2726–2735.
  • [6] Atagun A. O., Sezgin A. (2011). Soft substructures of rings, fields and modules, Comput. Math. Appl., 61, 592–601.
  • [7] Oguz, G., Gursoy, M.H., Icen, I.(2019). On soft topological categories. Hacet. J. Math. Stat., 48(6), 1675–1681.
  • [8] Shabir, M., Naz, M.(2011). On soft topological spaces. Comput. Math. Appl., 61(7), 1786–1799.
  • [9] Oguz, G. (2020). Soft Topological Transformation Groups. Mathematics, 8(9), 1545.
  • [10] Aygunoglu, A., Aygun, A.(2012). Some notes on soft topological spaces. Neural Comput. Appl., 22(1), 113–119.
  • [11] Oguz, G., Icen, I., Gursoy, M.H.(2020). A New Concept in the Soft Theory: Soft Groupoids. Southeast Asian Bull. Math., 44(4), 555–565.
  • [12] Yamak, S., Kazanci, O., Davvaz, B.(2011). Soft hyperstructure. Comput. Math. with Appl., 62(2), 797–803.
  • [13] Tasbozan H., Icen I., Bagrmaz, N. and Ozcan, A.F.(2017). Soft Sets and Soft Topology on Nearness Approximation Space, Filomat 31:13, 41174125.
  • [14] Oguz, G.(2020). A New View on Topological Polygroups. Turkish Journal of Science, 5(2), 110–117.
  • [15] Selvachandran, G., Salleh, A. R. (2013). Soft hypergroups and soft hypergroup homomorphism. In: AIP Conference Proceedings. American Institute of Physics, 1522(1), 821–827.
  • [16] Wang, J., Yin, M., Gu, W. (2011). Soft polygroups, Comput. Math. Appl., 62(9), 3529–3537.
  • [17] Selvachandran, G. (2015). Introduction to the theory of soft hyperrings and soft hyperring homomorphism. JP J. Algebra, Number Theory Appl., 36(3), 279–294.
  • [18] Shah, T., Shaheen, S. (2014). Soft topological groups and rings, Ann. Fuzzy Math. Inform., 7(5), 725–743.
  • [19] Davvaz, B., Leoreanu-Fotea, V. (2007). Hyperring theory and applications, International Academic Press, USA.
  • [20] Nodehi, M., Norouzi, M., Dehghan, O. R. (2020). An introduction to topological hyperrings. Casp. J. Math. Sci., 9(2), 210–223.
  • [21] Davvaz, B. (2004). Isomorphism theorems on hyperrings. Indian J. Pure Appl.Math., 35(3), 321–331.
  • [22] Velrajan, M., Asokkumar, A. (2010). Note on isomorphism theorems of hyperrings. Int. j. math. math. sci.,
  • [23] Maji,P.K., Roy, A.R., Biswas, R.(2002). An application of soft sets in a decision making problem, Comput. Math. Appl., 44, 1077–1083.
  • [24] Kazanci, O., Yilmaz, S., Yamak, S. (2010). Soft sets and soft BCH-algebras, Hacet. J. Math. Stat., 39, 205–217.
  • [25] Jinyan, W. A. N. G., Minghao, Y. . N., Wenxiang, G. U. (2015). Soft hyperrings and their (fuzzy) isomorphism theorems.Hacet. J. Math. Stat., 44(6), 1463–1475.
  • [26] Heidari,D. Davvaz,B. and Modarres, S. M. S. (2016). Topological polygroups, Bull. Malaysian Math. Sci. Soc., 39(2), 707-721.
There are 26 citations in total.

Details

Primary Language English
Journal Section Volume VI Issue I 2021
Authors

Abdullah Fatih Özcan 0000-0001-9732-8026

İlhan İçen 0000-0003-3576-0731

Hatice Taşbozan 0000-0002-6850-8658

Publication Date April 30, 2021
Published in Issue Year 2021 Volume: 6 Issue: 1

Cite

APA Özcan, A. F., İçen, İ., & Taşbozan, H. (2021). The Category of Soft Topological Hyperrings. Turkish Journal of Science, 6(1), 6-13.
AMA Özcan AF, İçen İ, Taşbozan H. The Category of Soft Topological Hyperrings. TJOS. April 2021;6(1):6-13.
Chicago Özcan, Abdullah Fatih, İlhan İçen, and Hatice Taşbozan. “The Category of Soft Topological Hyperrings”. Turkish Journal of Science 6, no. 1 (April 2021): 6-13.
EndNote Özcan AF, İçen İ, Taşbozan H (April 1, 2021) The Category of Soft Topological Hyperrings. Turkish Journal of Science 6 1 6–13.
IEEE A. F. Özcan, İ. İçen, and H. Taşbozan, “The Category of Soft Topological Hyperrings”, TJOS, vol. 6, no. 1, pp. 6–13, 2021.
ISNAD Özcan, Abdullah Fatih et al. “The Category of Soft Topological Hyperrings”. Turkish Journal of Science 6/1 (April 2021), 6-13.
JAMA Özcan AF, İçen İ, Taşbozan H. The Category of Soft Topological Hyperrings. TJOS. 2021;6:6–13.
MLA Özcan, Abdullah Fatih et al. “The Category of Soft Topological Hyperrings”. Turkish Journal of Science, vol. 6, no. 1, 2021, pp. 6-13.
Vancouver Özcan AF, İçen İ, Taşbozan H. The Category of Soft Topological Hyperrings. TJOS. 2021;6(1):6-13.