The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
권호 표지
DOI QR코드

DOI QR Code

CONSTRUCTION OF AN HV-BE-ALGEBRA FROM A BE-ALGEBRA BASED ON "BEGINS LEMMA"

  • Naghibi, R. (Department of Mathematics, Yazd University) ;
  • Anvariyeh, S.M. (Department of Mathematics, Yazd University) ;
  • Mirvakili, S. (Department of Mathematics, Payame Noor University)
  • Received : 2020.11.05
  • Accepted : 2021.08.17
  • Published : 2021.08.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, first we introduce the new class of HV-BE-algebra as a generalization of a (hyper) BE-algebra and prove some basic results and present several examples. Then, we construct the HV-BE-algebra associated to a BE-algebra (namely BL-BE-algebra) based on "Begins lemma" and investigate it.

Keywords

References

  1. S.S. Ahn, Y.H. Kim & J.M. Ko: Filters in commutative BE-algebras. Commun. Korean Math. Soc. 27 (2012), 233-242. https://doi.org/10.4134/CKMS.2012.27.2.233
  2. R.A. Borzooei, A. Borumand Saeid, A. Rezaei, A. Radfar & R. Ameri: On pseudo BE-algebras. Discussi. Math. General Algebra Appl. 33 (2013), 95-108. https://doi.org/10.7151/dmgaa.1193
  3. J. Chvalina: Functional graphs, quasi-ordered sets and commutative hypergroups. Masaryk University, Brno, 1995 (in Czech).
  4. P. Corsini & V. Leoreanu: Applications of hyperstructure theory. in: Adv. Math., vol. 5, Kluwer Academic Publishers, 2003.
  5. P. Corsini: Hyperstrutures associated with ordered sets. Bull. Greek Math. Soc. 48 (2003), 7-18.
  6. P. Corsini: Prolegomena of hypergroup theory. Second Edition, Aviani Editor, 1993.
  7. B. Davvaz: A brief survey of the theory of HV-structures. Proc. 8th International Congress on Algebraic Hyperstructures and Applications, 1-9 Sep., 2002, Samothraki, Greece, Spanidis Press (2003), 39-70.
  8. B. Davvaz & V. Leoreanu: Hyperring theory and applications. International Academic Press, Palm Harbor, USA, 2007.
  9. B. Davvaz: Partial abelian HV-monoids. Bull. Greek Math. Soc. 45 (2002), 53-62.
  10. M. Ghadiri & B. Davvaz: Direct system and direct limit of HV-modules. Iran. J. Sci. & Tech. Tran. A 28 (2004), 267-275.
  11. S.H. Ghazavi & S.M. Anvariyeh: EL-hyperstructures associated to n-ary relations. Soft Comput. 21 (2017), no. 19, 5841-5850. https://doi.org/10.1007/s00500-016-2165-3
  12. S.H. Ghazavi, S.M. Anvariyeh & S. Mirvakili: EL2-hyperstructures derived from (partially) quasi ordered hyperstructures. Iran. J. Math. Sci. Inform. 10 (2015), no. 2, 99-114.
  13. S.H. Ghazavi, S.M. Anvariyeh & S. Mirvakili: Ideals in EL-semihypergroups associated to ordered semigroups. J. Algebr. Syst. 3 (2015), no. 2, 109-125.
  14. D. Heidari & B. Davvaz: On ordered hyperstructures. U. P. B. Sci. Bull. Series A 73 (2011), no. 2, 85-96.
  15. S. Hoskova: Binary hyperstructure determined by relational and transformation systems. Habilitation Thesis, Faculty of Science, University of Ostrava, 2008.
  16. S. Hoskova: Order Hypergroups-The unique square root condition for quasi-order hypergroups. Set-valued Math. Appl. 1 (2008), 1-7.
  17. K. Iseki & S. Tanaka: An introduction to the theory of BCK-algebras. Math. Japonica 23 (1978), 1-26.
  18. Y.B. Jun, E.H. Roh & H.S. Kim: On BH-algebras. Sci. Math. Japonica Online 1 (1998), 347-354.
  19. Y.B. Jun, M.M. Zahedi, X.L. Lin & R.A. Borzooei: On hyper BCK-algebras. Ital. j. Pure Appl. Math. 8 (2000), 127-136.
  20. H.S. Kim & Y.H. Kim: On BE-algebras. Sci. Math. Jpn. 66 (2007), 113-116.
  21. F. Marty: Sur une generalization de la notion de group. 8th congress Math. Scandinaves, Stockholm (1934), 45-49.
  22. J. Neggers & H.S. Kim: On d-algebras. Math. Slovaca 49 (1999), 19-26.
  23. M. Novak: EL-hyperstructures: an overview. Ratio Math. 23 (2012), 65-80.
  24. M. Novak: Important elements of EL-hyperstructures. in: APLIMAT:10th International Conference, STU in Bratislava, Bratislava (2011), 151-158.
  25. M. Novak: On EL-semihypergroup. European J. Combin. 44 (2015), 274-286. https://doi.org/10.1016/j.ejc.2014.08.014
  26. M. Novak: Potential of the Ends lemma to create ring-like hyperstructures from quasi-ordered (semi)groups. South Bohemia Math. Lett. 17 (2009), no. 1, 39-50.
  27. M. Novak: The Notion of subhyperstructure of "Ends lemma"-based Hyperstructures. Aplimat-J. Appl. Math. 3 (2010), no. 2, 237-247.
  28. S. Omidi & B. Davvaz: On ordered Krasner hyperrings. Iran. J. Math. Sci. Inf. 12 (2017), no, 2, 35-49.
  29. A. Radfar, A. Rezaei & A. Borumand Saeid: Hyper BE-algebras. Novi Sad J. Math. 44 (2014), no. 2, 137-147.
  30. A. Rezaei & A. Borumand Saeid: Commutative ideals in BE-algebras. Kyungpook Math. J. 52 (2012), 483-494. https://doi.org/10.5666/KMJ.2012.52.4.483
  31. A. Rezaei, A. Borumand Saeid & R.A. Borzooei: Relation between Hilbert algebras and BE-algebras. Appl. Math. 8 (2013), 573-584.
  32. I.G. Rosenberg: Hypergroups and join spaces determined by relations. Ital. J. Pure Appl. Math. 4 (1998), 93-101.
  33. S. Spartalis: On HV-semigroups. Ital. J. Pure Appl. Math. 11 (2002), 165-174.
  34. S. Spartaiis: On reversible HV-groups. Algebraic Hyperstructures and Applications, Proc. Fifth Intefnat. Congress on AHA Iasi, Romania 1993. Hadronic Press, Inc. Palm Harbor (1994), 163-170.
  35. S. Spartalis: On the number of HV-rings with P-hyperoperations. Combinatorics (Acireale, 1992), Discrete Math. 155 (1996), 225-231. https://doi.org/10.1016/0012-365X(94)00386-W
  36. T. Vougiouklis: Generalization of P-hypergroups. Rend. Circ. Mat. Palermo 36(II) (1987), 114-121. https://doi.org/10.1007/BF02844705
  37. T. Vougiouklis: HV-vector spaces. Proc. 5th International Congress on Algebraic Hyperstructures and Applications, Jasi, Romania, July 4-10, 1993, Hadronic Press, Inc. Palm Harbor (1994), 181-190.
  38. T. Vougiouklis: Hyperstructures and their Representations. Hadronic Press, Inc. Palm Harbor, 1994.
  39. T. Vougiouklis: The fundamental relation in hyperrings. The general hyperfield. Algebraic hyperstructures and applications (Xanthi, 1990), 203-211, World Sci. Publishing, Teaneck, NJ, 1991.