Browsing by Author "Toksoy, Sultan Eylem"

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Citation - WoS: 11
Citation - Scopus: 12
Cofinitely Supplemented Modular Lattices
(SPRINGER HEIDELBERG, 2011) Rafail Alizade; Sultan Eylem Toksoy; 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 boolean OR b = 1 there exists an element c of b/0 such that a boolean OR c = 1 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: 3
Citation - Scopus: 1
Pure-direct-projective modules
(WORLD SCIENTIFIC PUBL CO PTE LTD, 2024) Rafail Alizade; Sultan Eylem Toksoy; Alizade, Rafail; Toksoy, Sultan Eylem
In this paper we introduce and study the pure-direct-projective modules that is the modules M every pure submodule A of which with M/A isomorphic to a direct summand of M is a direct summand of M. We characterize rings over which every right R-module is pure-direct-projective. We examine for which rings or under what conditions pure-direct-projective right R-modules are direct-projective projective quasi-projective pure-projective flat or injective. We prove that over a Noetherian ring every injective module is pure-direct-projective and a right hereditary ring R is right Noetherian if and only if every injective right R-module is pure-direct-projective. We obtain some properties of pure-direct-projective right R-modules which have DPSP and DPIP.