$\omega$-filters of distributive lattices

Document Type : Research Paper


1 Department of Mathematics, MVGR College of Engineering, Vizianagaram, Andhra Pradesh-535005, India.

2 Department of Mathematics, Albert Einstein School of Physical Sciences, Assam University, Silchar, Assam-788011, India.


The notion of $\omega$-filters is introduced in distributive lattices and their properties are studied. A set of equivalent conditions is derived for every maximal filter of a distributive lattice to become an $\omega$-filter which leads to a characterization of quasi-complemented lattices. Some sufficient conditions are derived for proper $D$-filters of a distributive lattice to become an $\omega$-filter. Finally, $\omega$-filters of a distributive lattice are characterized with the help of minimal prime $D$-filters.


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