$\omega$-filters of distributive lattices

نویسندگان
Venkata Rao, Chukka ID 1
Sambasiva Rao, Mukkamala ID 2

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

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

doi
10.22034/as.2021.2553
چکیده

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.

کلیدواژه‌ها
Prime $D$-filter, Minimal prime $D$-filter, Maximal filter, $omega$-filter, Quasi-complemented lattice, Boolean algebra