International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 12, Pages 801-806

Positive implicative ordered filters of implicative semigroups

Young Bae Jun1 and Kyung Ho Kim2

1Department of Mathematics Education, Gyeongsang National University, Chinju 660-701, Korea
2Department of Mathematics, Chungju National University, Chungju 380-702, Korea

Received 10 August 1999

Copyright © 2000 Young Bae Jun and Kyung Ho Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.