Boosters and Filters in MS-Almost Distributive Lattices
Yeshiwas Mebrat Gubena, Teferi Getachew Alemayehu · Communications in Mathematics and Applications · 2022
This paper deals on boosters and \(\beta\)-filters in MS-almost distributive lattice \(M\). It is proved that the set of all boosters in \(M\) is a bounded distributive lattice. Characterization of \(\beta\)-filters of $M$ in terms of boosters is established and a dual homomorphism of \(M\) and the set of all boosters of \(M\) is derived. Further, it is shown that every filter in \(M\) is an \(e\)-filter and every maximal filter in \(M\) is a \(\beta\)-filter. Equivalent conditions on which the set of all boosters is a relatively complemented lattice are established.