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Browsing by Author "Büyükaşık, Engin"
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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. 
Rugged modules: The opposite of flatness
Büyükaşık, Engin; Enochs, Edgar; Rozas, J. R. García; Kafkas Demirci, Gizem; LópezPermouth, Sergio; Oyonarte, Luis (Taylor & Francis Group, 201802)Relative notions of flatness are introduced as a mean to gauge the extent of the flatness of any given module. Every module is thus endowed with a flatness domain and, for every ring, the collection of flatness domains of ... 
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 noncosingular modules
Alagöz, Yusuf (Izmir Institute of Technology, 2014)The main purpose of this thesis is to investigate the notion of strongly noncosingular modules. We call a right Rmodule M strongly noncosingular if for every nonzero right R module N and every nonzero homomorphismf : M ... 
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 ... 
Strongly tnoncosingular modules
Günyüz, Ozan (Izmir Institute of Technology, 2010)This thesis is mainly concerned with the Tnoncosingularity issue of a module. Derya Keskin Tutuncu and Rachid Tribak introduced the Tnoncosingular modules and gave some properties of these modules. A moduleM is said to ... 
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 ...