DOI QR코드

DOI QR Code

ON QUASI-LATTICE IMPLICATION ALGEBRAS

YON, YONG HO

  • Received : 2015.04.21
  • Accepted : 2015.06.29
  • Published : 2015.09.30

Abstract

The notion of quasi-lattice implication algebras is a generalization of lattice implication algebras. In this paper, we give an optimized definition of quasi-lattice implication algebra and show that this algebra is a distributive lattice and that this algebra is a lattice implication algebra. Also, we define a congruence relation ΦF induced by a filter F and show that every congruence relation on a quasi-lattice implication algebra is a congruence relation ΦF induced by a filter F.

Keywords

quasi-lattice implication algebras;lattice implication algebras;filters;congruence relations

References

  1. H. Zhu, J.B. Zhao and Y. Xu, The n-fold prime filter of residuated lattice implication algebra, J. Zhengzhou Univ. Nat. Sci. Ed. 40 (2008), 19-22.
  2. R.A. Borzooei and S.F. Hosseiny, Finite lattice implication algebras, Jordan J. Math. Stat. 6 (2013), 265-283.
  3. Y.B. Jun, Fantastic filters of lattice implication algebras, Int. J. Math. Sci 24 (2000), 277-281. https://doi.org/10.1155/S0161171200003926
  4. S.E. Kang and S.S. Ahn, Rough filters of BE-algebras, J. Appl. Math. & Informatics 30 (2012), 1023-1030.
  5. S.D. Lee and K.H. Kim, On derivations of lattice implication algebras, Ars Combin. 108 (2013), 279-288.
  6. J. Liu and Y. Xu, Lattice implication algebras and MV-algebras, Chinese Quart. J. Math. 14 (1999), 17-23.
  7. E. L. Marsden, A note on implicative models, Notre Dame J. Form. Log. XIV(1) (1973), 139-144. https://doi.org/10.1305/ndjfl/1093890823
  8. E.H. Roh, S.Y. Kim and Y.B. Jun, Some operations on lattice implication algebras, Int. J. Math. Sci. 27 (2001), 45-52. https://doi.org/10.1155/S0161171201006214
  9. Y. Xu, Lattice implication algebras, J. Southwest Jiaotong Univ. 1 (1993), 20-27.
  10. Y. Xu and K.Y. Qin, Lattice H implication algebras and lattice implication algebra classes, J. Hebei Mining and Civil Engineering Institute 3 (1992), 139-143.
  11. Y. Xu and K.Y. Qin, On filters of lattice implication algebras, J. Fuzzy Math. 1 (1993), 251-260.
  12. Y.H. Yon and K.H. Kim, On f-derivations of lattice implication algebras, Ars Combin. 110 (2013), 205-215.