Browsing Mathematics / Matematik by Author "Alizade, Rafail"
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Cocoatomically supplemented modules
Alizade, Rafail; Güngör, Serpil (Springer, 201712)It is shown that if a submodule N of M is cocoatomically supplemented and M/N has no maximal submodule, then M is a cocoatomically supplemented module. If a module M is cocoatomically supplemented, then every finitely ... 
Cofinitely supplemented modular lattices
Alizade, Rafail; Toksoy, Sultan Eylem (Springer, 201110)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, ... 
Cofinitely weak supplemented lattices
Alizade, Rafail; Toksoy, Sultan Eylem (Indian National Science Academy, 200910)In this paper it is shown that an Ecomplemented 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 ... 
Cofinitely weak supplemented modules
Alizade, Rafail; Büyükaşık, Engin (Taylor & Francis, 200311)We prove that a module M is cofinitely weak supplemented or briefly cws (i.e., every submodule N of M with M/N finitely generated, has a weak supplement) if and only if every maximal submodule has a weak supplement. If M ... 
Extensions of weakly supplemented modules
Alizade, Rafail; Büyükaşık, Engin (Mathematica Scandinavica, 2008)It is shown that weakly supplemented modules need not be closed under extension (i.e. if U and M/U are weakly supplemented then M need not be weakly supplemented). We prove that, if U has a weak supplement in M then M is ... 
Poor and pipoor Abelian groups
Alizade, Rafail; Büyükaşık, Engin (Taylor & Francis, 201701)In this paper, poor abelian groups are characterized. It is proved that an abelian group is poor if and only if its torsion part contains a direct summand isomorphic to (Formula presented.) , where P is the set of prime ... 
The proper class generated by weak supplements
Alizade, Rafail; Demirci, Yılmaz Mehmet; Durğun, Yılmaz; Pusat, Dilek (Taylor & Francis, 201401)We show that, for hereditary rings, the smallest proper classes containing respectively the classes of short exact sequences determined by small submodules, submodules that have supplements and weak supplement submodules ... 
Resolutions in cotorsion theories
Akıncı, Karen; Alizade, Rafail (American Institute of Physics Publising, 2010)We consider the λ (μ) and λ̄ (μ̄) dimensions of modules taken under a cotorsion theory (F, C) satisfying the Hereditary Condition, and establish some inequalities between the dimensions of the modules of a short exact ... 
Rings and modules characterized by opposites of injectivity
Alizade, Rafail; Büyükaşık, Engin; Er, Noyan (Elsevier, 201407)In a recent paper, Aydoǧdu and LópezPermouth have defined a module M to be Nsubinjective if every homomorphism N→M extends to some E(N)→M, where E(N) is the injective hull of N. Clearly, every module is subinjective ... 
Small supplements, weak supplements and proper classes
Alizade, Rafail; Büyükaşık, Engin; Durğun, Yılmaz (Hacettepe Üniversitesi, 2016)Let SS denote the class of short exact sequences E:0 → Af→ B → C → 0 of Rmodules and Rmodule homomorphisms such that f(A) has a small supplement in B i.e. there exists a submodule K of M such that f(A) + K = B and f(A) ... 
Special precovers in cotorsion theories
Akıncı, Karen D.; Alizade, Rafail (Cambridge University Press, 200206)A cotorsion theory is defined as a pair of classes Extorthogonal to each other. We give a hereditary condition (HC) which is satisfied by the (flat, cotorsion) cotorsion theory and give properties satisfied by arbitrary ...