Mathematics / Matematik
Permanent URI for this collectionhttps://hdl.handle.net/11147/8
Browse
4 results
Search Results
Article Noetherian and Artinian Lattices(Hindawi Publishing Corporation, 2012) Keskin Tütüncü, Derya; Toksoy, Sultan Eylem; Tribak, RachidIt is proved that if L is a complete modular lattice which is compactly generated, then Rad(L)/0 is Artinian if, and only if for every small element a of L, the sublattice a/0 is Artinian if, and only if L satisfies DCC on small elements.Article Absolute Co-Supplement and Absolute Co-Coclosed Modules(Hacettepe Üniversitesi, 2013) Tütüncü, Derya Keskin; Toksoy, Sultan EylemA module M is called an absolute co-coclosed (absolute co-supplement) module if whenever M ≅ T/X the submodule X of T is a coclosed (supplement) submodule of T. Rings for which all modules are absolute co-coclosed (absolute co-supplement) are precisely determined. We also investigate the rings whose (finitely generated) absolute co-supplement modules are projective. We show that a commutative domain R is a Dedekind domain if and only if every submodule of an absolute co-supplement R-module is absolute co-supplement. We also prove that the class Coclosed of all short exact sequences 0→A→B→C→0 such that A is a coclosed submodule of B is a proper class and every extension of an absolute co-coclosed module by an absolute co-coclosed module is absolute co-coclosed.Article Citation - WoS: 11Citation - Scopus: 11Cofinitely Supplemented Modular Lattices(Springer Verlag, 2011) Alizade, Rafail; Toksoy, Sultan EylemIn 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.Article Citation - WoS: 14Citation - Scopus: 14Cofinitely Weak Supplemented Lattices(Indian National Science Academy, 2009) Alizade, Rafail; Toksoy, Sultan EylemIn 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).