- Volume 33 Issue 5_6
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.
quasi-lattice implication algebras;lattice implication algebras;filters;congruence relations
- 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.
- R.A. Borzooei and S.F. Hosseiny, Finite lattice implication algebras, Jordan J. Math. Stat. 6 (2013), 265-283.
- Y.B. Jun, Fantastic filters of lattice implication algebras, Int. J. Math. Sci 24 (2000), 277-281. https://doi.org/10.1155/S0161171200003926
- S.E. Kang and S.S. Ahn, Rough filters of BE-algebras, J. Appl. Math. & Informatics 30 (2012), 1023-1030.
- S.D. Lee and K.H. Kim, On derivations of lattice implication algebras, Ars Combin. 108 (2013), 279-288.
- J. Liu and Y. Xu, Lattice implication algebras and MV-algebras, Chinese Quart. J. Math. 14 (1999), 17-23.
- 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
- 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
- Y. Xu, Lattice implication algebras, J. Southwest Jiaotong Univ. 1 (1993), 20-27.
- 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.
- Y. Xu and K.Y. Qin, On filters of lattice implication algebras, J. Fuzzy Math. 1 (1993), 251-260.
- Y.H. Yon and K.H. Kim, On f-derivations of lattice implication algebras, Ars Combin. 110 (2013), 205-215.