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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).
Citation - WoS: 10
Citation - Scopus: 10
Special Precovers in Cotorsion Theories
(Cambridge University Press, 2002) Akıncı, Karen D.; Alizade, Rafail
A cotorsion theory is defined as a pair of classes Ext-orthogonal to each other. We give a hereditary condition (HC) which is satisfied by the (flat, cotorsion) cotorsion theory and give properties satisfied by arbitrary cotorsion theories with an HC. Given a cotorsion theory with an HC, we consider the class of all modules having a special precover with respect to the first class in the cotorsion theory and show that this class is closed under extensions. We then raise the question of whether this class is resolving or coresolving.

Mathematics / Matematik