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Citation - WoS: 11
Citation - Scopus: 11
Cofinitely Supplemented Modular Lattices
(Springer Verlag, 2011) Alizade, Rafail; Toksoy, Sultan Eylem
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.
Citation - WoS: 14
Citation - Scopus: 14
Cofinitely Weak Supplemented Lattices
(Indian National Science Academy, 2009) Alizade, Rafail; Toksoy, Sultan Eylem
In this paper it is shown that an E-complemented complete modular lattice L with small radical is weakly supplemented if and only if it is semilocal. L is a cofinitely weak supplemented lattice if and only if every maximal element of L has a weak supplement in L. If )α/0 is a cofinitely weak supplemented (weakly supplemented) sublattice and 1/α has no maximal element (1/α is weakly supplemented and a has a weak supplement in L), then L is cofinitely weak supplemented (weakly supplemented).

Mathematics / Matematik