Refail AlizadeSultan Eylem Toksoy2025-10-0620112193567X, 219142811319-80252191-428110.1007/s13369-011-0095-zhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-80053358674&doi=10.1007%2Fs13369-011-0095-z&partnerID=40&md5=265333455a262d325c0955bb4596597bhttps://gcris.yasar.edu.tr/handle/123456789/10220In 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 v b there exists an element c of b/0 such that a v c 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. © 2011 King Fahd University of Petroleum and Minerals. © 2011 Elsevier B.V. All rights reserved.EnglishAmple Supplement, Amply Cofinitely Supplemented Lattice, Amply Supplemented Lattice, Cofinite Element, Cofinitely Supplemented LatticeArticle