Browsing by Author "Büyükaşık, Engin"
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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 ... 
Cocoatomically supplemented modules
Güngör, Serpil (Izmir Institute of Technology, 2013)The purpose of this study to define cocoatomically supplemented modules, cocoatomically supplemented modules, cocoatomically weak supplemented modules and cocoatomically amply supplemented modules and examine them over ... 
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 ... 
Homological objects of proper classes generated by simple modules
Durğun, Yılmaz (Izmir Institute of Technology, 2014)The main purpose of this thesis is to study some classes of modules determined by neat, coneat and spure submodules. A right Rmodule M is called neatflat (resp. coneatflat) if the kernel of any epimorphism Y → M → 0 ... 
Modules satisfying conditions that are opposites of absolute purity and flatness
Kafkas Demirci, Gizem (Izmir Institute of Technology, 201707)The main purpose of this thesis is to study the properties which are opposites of absolute pure and flat modules. A right module M is said to be test for flatness by subpurity (for short, t.f.b.s.) if its subpurity domain ... 
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 pseudo semisimple rings
Mutlu, Hatice (Izmir Institute of Technology, 2013)In this thesis, we give a survey of right pseudo semisimple rings and prove some new results about these rings. Namely, we prove that a right pseudo semisimple ring is an internal exchange ring and a right pseudo semisimple ... 
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 ... 
Operations on proper classes related to supplements
Demirci, Yılmaz Mehmet (Izmir Institute of Technology, 2012)The purpose of this study is to understand the properties of the operations +, ◦, and * defined on classes of short exact sequences and apply them to the proper classes related to supplements. The operation ◦ on classes ... 
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) ...