Communications of the
Korean Mathematical Society CKMS

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: implicative semigroup, ordered filter, implicative ordered filter

MSC numbers: 20M12, 06F05, 06A06, 06A12