@article{Hummdi2025, 
author = {Ali Yahya Hummdi and N. Rafi and M. Balaiah and Y. Monikarchana},
title = {Exploring prime    F  −filters of almost distributive lattices},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {11},
pages = {27519-27534},
keywords = {almost distributive lattice, F−filter, F−normal, totally ordered set, comaximal},
url = {https://www.sciopen.com/article/10.3934/math.20251210},
doi = {10.3934/math.20251210},
abstract = {The concept of        F    −filters is introduced in an almost distributive lattice(ADL) and their properties are studied. A set of equivalent conditions is established for every proper        F    −filter of an ADL to become a prime        F    −filter. For any        F    −filter        U   of an ADL,              O                      F              (      U    ) is defined, and it is proved that              O                      F              (      U    ) is an        F    −filter if        U   is prime. It is also derived that each minimal prime        F    −filter belonging to              O                      F              (      U    ) is contained in        U  , and              O                      F              (      U    ) is the intersection of all the minimal prime        F    −filters contained in        U    . The concept of        F    −normal ADL is defined and characterized in terms of the prime        F    −filters and minimal prime        F    −filters, as well as relative annihilators with respect to        F  .}
}