Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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IMPLICATIVE ORDERED FILTERS OF IMPLICATIVE SEMIGROUPS

  • Jun, Young-Bae (Department of Mathematics Education Gyeongsang National University)
  • Published : 1999.01.01
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Abstract

This paper continues the investigations of implicative semigroups and of their ordered filters which were started in general case by M.W. Chan and K. P. Shum [3]. In particular, the notion of an implicative ordered filter of an implicative semigroup is introduced. We state some equivalent conditions for an ordered filter to be an implicative ordered filter and obtain the so called extension property for implicative ordered filters.

Keywords

References

  1. Amer. Math. Sco. Coll. Publ. v.XXV Lattice Theory G. Birkhoff
  2. J. London Math. Soc. v.40 Pseudo-residuals in semigroups 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. Semigroup Forum v.54 On ordered filters of implicative semigroups Y.B. Jun;J. Meng;X.L. Xin
  6. Trans. Amer. Math. Soc. v.117 Implicative sedilattices W.C. Nemitz