Rafail AlizadeSultan Eylem ToksoyAlizade, RafailToksoy, Sultan Eylem2025-10-0620111319-80252191-428110.1007/s13369-011-0095-z2-s2.0-80053358674http://dx.doi.org/10.1007/s13369-011-0095-zhttps://gcris.yasar.edu.tr/handle/123456789/6617https://doi.org/10.1007/s13369-011-0095-zIn this paper it is shown that a lattice L is a cofinitely supplemented lattice if and only if every maximal element of L has a supplement in L. If a/0 is a cofinitely supplemented sublattice and 1/a has no maximal element then L is cofinitely supplemented. A lattice L is amply cofinitely supplemented if and only if every maximal element of L has ample supplements in L if and only if for every cofinite element a and an element b of L with a boolean OR b = 1 there exists an element c of b/0 such that a boolean OR c = 1 where c is the join of finite number of local elements of b/0. In particular a compact lattice L is amply supplemented if and only if every maximal element of L has ample supplements in L.Englishinfo:eu-repo/semantics/openAccessCofinite element, Ample supplement, Amply supplemented lattice, Cofinitely supplemented lattice, Amply cofinitely supplemented latticeAmple SupplementCofinitely Supplemented LatticeAmply Cofinitely Supplemented LatticeCofinite ElementAmply Supplemented LatticeArticle