Positive implicative ordered filters of implicative semigroups

• Main Authors: Young Bae Jun, Kyung Ho Kim
• Format: Article
• Language: English
• Published: Hindawi Limited 2000-01-01
• Series: International Journal of Mathematics and Mathematical Sciences
• Subjects: Implicative semigroup; ordered filter; (positive) implicative ordered filter.
• Online Access: http://dx.doi.org/10.1155/S0161171200003781

We introduce the notion of positive implicative ordered filters in implicative semigroups. We show that every positive implicative ordered filter is both an ordered filter and an implicative ordered filter. We give examples that an ordered filter (an implicative ordered filter) may not be a positive implicative ordered filter. We also give equivalent conditions of positive implicative ordered filters. Finally we establish the extension property for positive implicative ordered filters.