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International Journal of Mathematics and Mathematical Sciences
Volume 26, Issue 12, Pages 731-735
http://dx.doi.org/10.1155/S0161171201005579

Some results on ordered filters of implicative semigroups

Department of Mathematics Education, Gyeongsang National University, Jinju 660-701, Korea

Received 1 August 2000

Copyright © 2001 Hindawi Publishing Corporation. 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.

Abstract

We introduce a special set in an implicative semigroup. Using it, an equivalent condition of an ordered filter is stated. We prove that an ordered filter can be represented by the union of such sets.