Boosters and Filters in MS-Almost Distributive Lattices - Gubena, Yeshiwas Mebrat; Alemayehu, Teferi Getachew (Communications in Mathematics and Applications, 2022)
This paper deals on boosters and \(β\)-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 \(β\)-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 \(β\)-filter. Equivalent conditions on which the set of all boosters is a relatively complemented lattice are established.
Keywords: Booster; β-filter; ADL; MS-ADL; Maximal element