Transitive and Absorbent Filters of Implicative Almost Distributive Lattices

Berhanu Assaye Alaba, Mihret Alamneh, Tilahun Mekonnen Munie

Abstract


In this paper, we introduce the concept of transitive and absorbent filters of implicative almost distributive lattices and studied their properties. A necessary and sufficient condition is derived for every filter to become a transitive filter. Some sufficient conditions are also derived for a filter to become a transitive filter. A set of equivalent conditions is obtained for a filter to become an absorbent filter.

Keywords


Implicative almost distributive lattices; transitive filters; absorbent filters

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References


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DOI: http://dx.doi.org/10.12962/j24775401.v4i2.3597

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International Journal of Computing Science and Applied Mathematics by Department Mathematics ITS is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Based on a work at http://iptek.its.ac.id/index.php/ijcsam.