Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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LI-ideals in lattice implication algebras

  • Jun, Young-Bae (Department of Mathematics Education, Gyeongsang National University, Chinju 660-701) ;
  • Roh, Eun-Hwan (Department of Mathematics Education, Gyeongsang National University, Chinju 660-701) ;
  • Yang Xu
  • Published : 1998.02.01
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Abstract

We define an LI-ideal of a lattice implication algebra and show that every LI-ideal is a lattice ideal. We give an exampl that a lattice ideal may not be an LI-ideal, and show that every lattice ideal is an LI-ideal in a lattice H implication algebra. we discuss the relationship between filters and LI-ideals, and study how to generate an LI-ideal by a set. We construct the quotient structure by using an LI-ideal, and study the properties of LI-ideals related to implication homomorphisms.

Keywords

References

  1. A course in universal algebra Burris;H. P. Sankappanavar
  2. Bull. Korean Math. Soc v.34 Implicative filters of lattice implication algebras Y. B. Jun
  3. Proc. of 5thManyValued Logical Congress of China Homomorphisms in lattice implication algebras Y. Xu
  4. J. Southwest Jiaotong University v.1 Lattice implication algebras Y. Xu
  5. J. Hebei Mining and Civil Engineering Institute v.3 Lattice H implication algebras and lattice implication algebra classes Y. Xu;K. Y. Qin
  6. J. FuzzyMath v.1 On filters of lattice implication algebras Y. Xu;K. Y. Qin