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Keywords:
filter; co-annihilator; coaxial filter; strongly coaxial filter; $pm$-lattice; normal prime filter
filter; co-annihilator; coaxial filter; strongly coaxial filter; $pm$-lattice; normal prime filter
Summary:
Coaxial filters and strongly coaxial filters are introduced in distributive lattices and some characterization theorems of $pm$-lattices are given in terms of co-annihilators. Some properties of coaxial filters of distributive lattices are studied. The concept of normal prime filters is introduced and certain properties of coaxial filters are investigated. Some equivalent conditions are derived for the class of all strongly coaxial filters to become a sublattice of the filter lattice.
References:
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