Positive implicative ordered filters of implicative semigroups

摘要

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