Search Results

Now showing 1 - 1 of 1

Citation - WoS: 11
Citation - Scopus: 11
Cofinitely Supplemented Modular Lattices
(Springer Verlag, 2011) Alizade, Rafail; Alizade, Rafail; Toksoy, Sultan Eylem; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
In 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.

WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection