Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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Positive implicative and associative filters of lattice implication algebras

  • Jun, Young-Bae (Department of Mathematics, Gyeongsang National University, Chinju 660-701) ;
  • Yang Xu (Department of Applied Mathematics, Southwest Jiaotong University, Chengdu, Sichuan 610031, pp. R. China) ;
  • Keyun Qin (Department of Mathematics, Henan Normal University, Xinxiang, Henan 453002, pp. R. China)
  • Published : 1998.02.01
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Abstract

We introduce the concepts of a positive implicative filter and an associative filter in a lattice implication algebra. We prove that (i) every positive implicative filter is an implicative filter, and (ii) every associative filter is a filter. We provide equivalent conditions for both a positive implicative filter and an associative filter.

Keywords

References

  1. Bull. Korean Math. v.34 Implicative filters of lattice implication algebras Y. B. Jun
  2. submitted Fuzzy filters of lattice implication algebras Y. B. Jun;Y. Xu
  3. Proc. of 5thManyValued Logical Congress of China Homomorphisms in lattice implication algebras Y. Xu
  4. J. of Southwest Jiaotong Univ v.1 Lattice implication algebras Y. Xu
  5. J. Fuzzy Math v.1 On filters of lattice implication algebras Y. Xu;K. Y. Qin
  6. Fuzzy Sets and Systems v.35 Fuzzy ideals on a distributive lattice B. Yuan;;W. Wu