w−FILTERS OF ALMOST DISTRIBUTIVE LATTICES

The notion of w−filters is introduced in an Almost Distributive Lattice(ADL) and properties are investigated. A necessary and sufficient condition is derived for a maximal filter of an ADL to become a w−filter which leads to a characterization of a quasi-complemented ADL. Also, w−filters of an ADL are characterized in terms of minimal prime D−filters.

کلیدواژه ها:

Almost Distributive Lattice(ADL) ، Quasi-complemented ADL ، prime ideal ، D−filter ، w−filter