DOI QR코드

DOI QR Code

MIRROR d-ALGEBRAS

  • So, Keum Sook (Department of Mathematics, Chungbuk National University) ;
  • Kim, Young Hee (Department of Mathematics, Hallym University)
  • Received : 2012.10.03
  • Accepted : 2012.12.02
  • Published : 2013.05.30

Abstract

In this paper we investigate necessary conditions for the mirror algebra $(M(X),{\bigoplus},(0,0))$ to be a $d$-algebra (having the condition (D5), resp.) when (X, *, 0) is a d-algebra (having the condition (D5), resp.). Moreover, we obtain the necessary conditions for M(X) of a $d^*$-algebra X to be a $d^*$-algebra.

Keywords

References

  1. S.S. Ahn and H.S. Kim, On QS-algebras, Chungcheong Math. J. 12(1999), 33-41.
  2. S.S. Ahn, H.S. Kim and H.D. Lee, R-maps and L-maps in Q-algebras, Int. J. Math. Pure Appl. Math. 12(2004), 419-425.
  3. P.J. Allen, H.S. Kim and J. Neggers, On companion d-algebras, Math. Slovaca 57 (2007), 93-106. https://doi.org/10.2478/s12175-007-0001-z
  4. P.J. Allen, H.S. Kim and J. Neggers, Deformations of d/BCK-algebras, Bull. Korean Math. Soc. (to appear). https://doi.org/10.4134/BKMS.2011.48.2.315
  5. P.J. Allen, H.S. Kim and J. Neggers, L-up and mirror algebras, Sci. Math. Japonica. 59 (2004), 605-612.
  6. A. Iorgulescu, Algebras of logic as BCK-algebras, Editura ASE, Bucharest, 2008.
  7. K. Iseki, On BCI-algebras, Math. Seminar Notes 8 (1980), 125-130.
  8. K. Iseki and S. Tanaka, An introduction to theory of BCK-algebras, Math. Japonica 23 (1978), 1-26.
  9. J. Meng and Y.B. Jun, BCK-algebras, Kyungmoon Sa, Seoul, 1994.
  10. J. Neggers, S.S. Ahn and H.S. Kim, On Q-algebras, Int. J. Math. and Math. Sci. 27 (2001), 749-757. https://doi.org/10.1155/S0161171201006627
  11. J. Neggers, A. Dvurecenskij and H.S. Kim, On d-fuzzy functions in d-algebras, Foundation of Physics 30 (2000), 1805-1815.
  12. J. Neggers, Y.B. Jun and H.S. Kim, On d-ideals in d-algebras, Math. Slovaca 49 (1999), 243-251.
  13. J. Neggers and H.S. Kim, On d-algebras, Math. Slovaca 49 (1999), 19-26.
  14. K.S. So, A contruction of mirror Q-algebras, Int. J. Math. & Math. Sci., 2011 (2011), Art. ID 219496.
  15. H. Yisheng, BCI-algebras, Science Press, Beijing, 2006.

Cited by

  1. FILTERS OF BE-ALGEBRAS WITH RESPECT TO A CONGRUENCE vol.34, pp.1_2, 2016, https://doi.org/10.14317/jami.2016.001
  2. ON MEDIAL B-ALGEBRAS vol.32, pp.5_6, 2014, https://doi.org/10.14317/jami.2014.849
  3. INT-SOFT POSITIVE IMPLICATIVE FILTERS IN BE-ALGEBRAS vol.33, pp.3_4, 2015, https://doi.org/10.14317/jami.2015.459