Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

DERIVATIONS OF MV-ALGEBRAS FROM HYPER MV-ALGEBRAS

  • Hamidi, M. (Department of Mathematics, Payame Noor University) ;
  • Borzooei, R.A. (Department of Mathematics, Shahid Beheshti University)
  • Received : 2015.10.27
  • Accepted : 2016.09.05
  • Published : 2016.09.25
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we investigate some new results in MV-algebras and (strong) hyper MV-algebras. We show that for any infinite countable set M, we can construct an MV-algebra and a strong hyper MV-algebra on M. Specially, for any infinite totally bounded set, we can construct a strong hyper MV-algebra on it. Then by considering the concept of fundamental relation on hyper MV-algebras, we define the notion of fundamental MV-algebra and prove that any MV-algebra is a fundamental MV-algebra. In practical, we show that any infinite countable MV-algebra is a fundamental MV-algebra of itself, but it is not correct for finite MV-algebras.

Keywords

References

  1. R. A. Borzooei, R. Ameri and M. Hamidi, Fundamental Relation on Hyper BCK-algebras, An. Univ. Oradea fasc. Mat., Tom XXI, 1 (2014), 123-137.
  2. C. C. Chang, Algebraic analysis of many valued logics, Trans. Amer. Math. Soc., 88 (1958) 467-490. https://doi.org/10.1090/S0002-9947-1958-0094302-9
  3. R. Cignoli, I. M. L. Dottaviano and D. Mundici, Algebraic Foundations of many-valued Reasoning, Kluwer., 2000.
  4. P. Corsini, Prolegomena of Hypergroup theory, Second Edition, Aviani Editor., 1993.
  5. Sh. Ghorbani, A. Hasankhani and E. Eslami, Hyper MV-algebras, Set-Valued Math. and Apl., 1(2) (2008), 205-222.
  6. Sh. Ghorbani, E. Eslami, and A. Hasankhani, Quotient hyper MV-algebras, Sci Math. Jpn., 66(3) (2007), 371-386.
  7. Sh. Ghorbani, A. Hasankhani, and E. Eslami, Hyper MV-algebras, Set-Valued Math. Appl., 1 (2008), 205-222.
  8. P. R. Halmos, Naive Set Theory, Springer-Verlag, New York., 1974.
  9. Y. Imai and K. Iseki, On Axiom Systems of Propositional Calculi, XIV, Proc. Japan Acad., 42 (1966), 19-22. https://doi.org/10.3792/pja/1195522169
  10. T. Jech, Set Theory, The 3rd Millennium Edition, Springer Monographs in Mathematics., 2002.
  11. Y. B. Jun, M. S. Kang, and H. S. Kim, Hyper MV-deductive systems of hyper MV-algebras, Commun. Korean Math. Soc., 25(4) (2010), 537-545. https://doi.org/10.4134/CKMS.2010.25.4.537
  12. F. Marty, Sur une Generalization de la Notion de Groupe, 8th Congres Math. Scandinaves, Stockholm,. (1934), 45-49.
  13. S. Rasouli, D. Heidari and B. Davvaz, $\eta$-Relations and Transitivity Conditions of $\eta$ on Hyper-MV Algebras, J. Mult.-Valued Logic Soft Comput., 15 (2009), 517-524.
  14. S. Rasouli, D. Heidari and B. Davvaz, Homomorphism, Ideals and Binary Relations on Hyper-MV Algebras, J. Mult.-Valued Logic Soft Comput., 17 (2011), 47-68.
  15. L. Torkzadeh and A. Ahadpanah, Hyper MV -ideals in hyper MV -algebras, MLQ Math. Log. Q., 56(1) (2010), 51-62. https://doi.org/10.1002/malq.200810035
  16. T. Vougiouklis, Hyperstructures and their representations, Hadronic Press Inc., 1994.