Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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A note on ordered filters of implicative semigroups

  • Jun, Young-Bae (Department of Mathematics Education, Gyeongsang National University, Chinju 660-701)
  • Published : 1997.05.01
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Abstract

The notions of implicative semigroup and ordered filter were introduced by M. W. Chan and K. pp. Shum [3]. The first is a generalization of implicative semilattice (see W. C. Nemitz [6] and T. S. Blyth [2]) and has a close relation with the implication in mathematical logic and set theoretic difference (see G. Birkhoff [1] and H. B. Curry [4]). For the general development of implicative semilattice theory the ordered filters play an important role, which is shown by W. C. Nemitz [6].

Keywords

References

  1. Amer. Math. Soc. Coll. Publ v.XXV Lattice Theory G. Birkhoff
  2. J. London Math. Soc. v.40 Pseudoresidual T. S. Blyth
  3. Semigroup Forum v.46 Homomorphisms of implicative semigroups M.W. Chan;K. P. Shum
  4. Foundations of Mathematics Logic H. B. Curry
  5. On ordered filters of implicative semigroups, to appear in Semigroup Forum Y. B. Jun;J. Meng;X. L. Xin
  6. Trans. Amer. Math. Soc. v.117 Implicative semilattices W. C. Nemitz