Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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SOME CONSTRUCTIONS OF IMPLICATIVE/COMMUTATIVE d-ALGEBRAS

  • Ahn, Sun-Shin (DEPARTMENT OF MATHEMATICS EDUCATION DONGGUK UNIVERSITY) ;
  • Kim, Young-Hee (DEPARTMENT OF MATHEMATICS CHUNGBUK NATIONAL UNIVERSITY)
  • Published : 2009.01.31
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Abstract

In this paper, we give some constructions of implicative/commutative d-algebras which are not BCK-algebras. This demonstrate that the notion of implicative/commutative d-algebras are indeed generalizations of the same in BCK-algebras.

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References

  1. P. J. Allen, H. S. Kim, and J. Neggers, Companion d-algebras, Math. Slovaca 57 (2007), no. 2, 93-106. https://doi.org/10.2478/s12175-007-0001-z
  2. G. Georgescu and A. Iorgulescu, Pseudo-BCK algebras: an extension of BCK algebras, Combinatorics, computability and logic (Constanta, 2001), 97-114, Springer Ser. Dis- crete Math. Theor. Comput. Sci., Springer, London, 2001.
  3. J. S. Han, H. S. Kim, and J. Neggers, Strong and ordinary d-algebras, J. Mutiple-Valued Logic and Soft Computing, (to appear)
  4. Y. Huang, BCI-algebras, Science Press, Beijing, 2003.
  5. K. Iseki, On BCI-algebras, Math. Sem. Notes Kobe Univ. 8 (1980), no. 1, 125-130.
  6. K. Iseki and S. Tanaka, An introduction to the theory of BCK-algebras, Math. Japon. 23 (1978/79), no. 1, 1-26.
  7. Y. C. Lee and H. S. Kim, On d^{\ast}-subalgebras of d-transitive d^{\ast}-algebras, Math. Slovaca 49 (1999), no. 1, 27-33.
  8. J. Meng, Implicative commutative semigroups are equivalent to a class of BCK algebras, Semigroup Forum 50 (1995), no. 1, 89-96. https://doi.org/10.1007/BF02573506
  9. J. Meng and Y. B. Jun, BCK-algebras, Kyungmoon Sa, Korea, 1994.
  10. D. Mundici, MV-algebras are categorically equivalent to bounded commutative BCKalgebras , Math. Japon. 31 (1986), no. 6, 889-894.
  11. J. Neggers, A. Dvurecenskij, and H. S. Kim, On d-fuzzy functions in d-algebras, Invited papers dedicated to Maria Luisa Dalla Chiara, Part II. Found. Phys. 30 (2000), no. 10, 1807-1816. https://doi.org/10.1023/A:1026466720971
  12. J. Neggers and H. S. Kim, On d-algebras, Math. Slovaca 49 (1999), no. 1, 19-26.
  13. J. Neggers, Y. B. Jun, and H. S. Kim, On d-ideals in d-algebras, Math. Slovaca 49 (1999), no. 3, 243-251.
  14. Z. Riecanova, On embeddings of generalized effect algebras into complete effect algebras, Soft Computing 10 (2006), 476-482. https://doi.org/10.1007/s00500-005-0521-9
  15. X. H. Zhang and W. H. Li, On pseudo-BL algebras and BCC-algebras, Soft Computing 10 (2006), 941-952. https://doi.org/10.1007/s00500-005-0021-y

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  2. d-ALGEBRAS WITH COMPLICATED CONDITION vol.31, pp.4, 2009, https://doi.org/10.5831/HMJ.2009.31.4.489