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Absolutely spure modules and neatflat modules
Büyükaşık, Engin; Durğun, Yılmaz (Taylor & Francis, 201502)Let R be a ring with an identity element. We prove that R is right Kasch if and only if injective hull of every simple right Rmodules is neatflat if and only if every absolutely pure right Rmodule is neatflat. A ... 
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 ... 
Coneat submodules and coneatflat modules
Büyükaşık, Engin; Durǧun, Yılmaz (Korean Mathematical Society, 2014)A submodule N of a right Rmodule M is called coneat if for every simple right Rmodule S, any homomorphism N → S can be extended to a homomorphism M → S. M is called coneatflat if the kernel of any epimorphism Y → M → 0 ... 
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 ... 
Modules whose maximal submodules are supplements
Büyükaşık, Engin; Pusat, Dilek (Hacettepe Üniversitesi, 2010)We study modules whose maximal submodules are supplements (direct summands). For a locally projective module, we prove that every maximal submodule is a direct summand if and only if it is semisimple and projective. We ... 
Neatflat modules
Büyükaşık, Engin; Durğun, Yılmaz (Taylor & Francis, 201601)Let R be a ring. A right Rmodule M is said to be neatflat if the kernel of any epimorphism Y → M is neat in Y, i.e., the induced map Hom(S, Y) → Hom(S, M) is surjective for any simple right Rmodule S. Neatflat right ... 
On a recent generalization of semiperfect rings
Büyükaşık, Engin; Christian, Lomp (Cambridge University Press, 200810)In a recent paper by Wang and Ding, it was stated that any ring which is generalized supplemented as a left module over itself is semiperfect. The purpose of this note is to show that Wang and Ding's claim is not true and ... 
On pseudo semisimple rings
Büyükaşık, Engin; Mohamed, Saad H.; Mutlu, Hatice (World Scientific Publishing, 201303)A necessary and sufficient condition is obtained for a right pseudo semisimple ring to be left pseudo semisimple. It is proved that a right pseudo semisimple ring is an internal exchange ring. It is also proved that a right ... 
On wlocal modules and Radsupplemented modules
Büyükaşık, Engin; Tribak, Rachid (Korean Mathematical Society, 2014)All modules considered in this note are over associative commutative rings with an identity element. We show that a wlocal module M is Radsupplemented if and only if M/P(M) is a local module, where P(M) is the sum of all ... 
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 ... 
Radsupplemented modules
Büyükaşık, Engin; Mermut, Engin; Özdemir, Salahattin (Universita di Padova, 2010)Let τ be a radical for the category of left Rmodules for a ring R. If M is a τcoatomic module, that is, if M has no nonzero τtorsion factor module, then τ(M) is small in M. If V is a τsupplement in M, then the intersection ... 
Radsupplements in injective modules
Büyükaşık, Engin; Tribak, Rachid (Lugansk Taras Shevchenko National University, 2016)We introduce and study the notion of Radsinjective modules (i.e. modules which are Radsupplements in their injective hulls). We compare this notion with another generalization of injective modules. We show that the class ... 
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 ... 
Rings over which flat covers of simple modules are projective
Büyükaşık, Engin (World Scientific Publishing, 201206)Let R be a ring with identity. We prove that, the flat cover of any simple right Rmodule is projective if and only if R is semilocal and J(R) is cotorsion if and only if R is semilocal and any indecomposable flat right ... 
Rings whose modules are weakly supplemented are perfect. Applications to certain ring extensions
Büyükaşık, Engin; Lomp, Christian (Mathematica Scandinavica, 2009)In this note we show that a ring R is left perfect if and only if every left Rmodule is weakly supplemented if and only if R is semilocal and the radical of the countably infinite free left Rmodule has a weak supplement. 
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) ... 
Strongly radical supplemented modules
Büyükaşık, Engin; Türkmen, Ergül (Springer, 201201)Zöschinger studied modules whose radicals have supplements and called these modules radical supplemented. Motivated by this, we call a module strongly radical supplemented (briefly srs) if every submodule containing the ... 
Weakly distributive modules. Applications to supplement submodules
Büyükaşık, Engin; Demirci, Yılmaz Mehmet (Indian Academy of Sciences, 201011)In this paper, we define and study weakly distributive modules as a proper generalization of distributive modules. We prove that, weakly distributive supplemented modules are amply supplemented. In a weakly distributive ... 
When δsemiperfect rings are semiperfect
Büyükaşık, Engin; Lomp, Christian (TÜBİTAK, 201009)Zhou defined δ semiperfect rings as a proper generalization of semiperfect rings. The purpose of this paper is to discuss relative notions of supplemented modules and to show that the semiperfect rings are precisely the ...