International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 12, Pages 801-806
Positive implicative ordered filters of implicative semigroups
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.