Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

Permanent URI for this collectionhttps://hdl.handle.net/11147/7148

Browse

Filters

2008 - 200912010 - 2019112020 - 20234

Settings

Institution Author: search.filters.institutionAuthor.Büyükaşık, EnginScopus Q: search.filters.scopusQuartile.Q3

Search Results

Now showing 1 - 10 of 16
  • Article
    Citation - WoS: 3
    Citation - Scopus: 3
    Dual Kasch rings
    (World Scientific Publishing, 2023) Lomp, Christian; Büyükaşık, Engin; Yurtsever, Haydar Baran
    It is well known that a ring R is right Kasch if each simple right R-module embeds in a projective right R-module. In this paper we study the dual notion and call a ring R right dual Kasch if each simple right R-module is a homomorphic image of an injective right R-module. We prove that R is right dual Kasch if and only if every finitely generated projective right R-module is coclosed in its injective hull. Typical examples of dual Kasch rings are self-injective rings, V-rings and commutative perfect rings. Skew group rings of dual Kasch rings by finite groups are dual Kasch if the order of the group is invertible. Many examples are given to separate the notion of Kasch and dual Kasch rings. It is shown that commutative Kasch rings are dual Kasch, and a commutative ring with finite Goldie dimension is dual Kasch if and only if it is a classical ring (i.e. every element is a zero divisor or invertible). We obtain that, for a field k, a finite dimensional k-algebra is right dual Kasch if and only if it is left Kasch. We also discuss the rings over which every simple right module is a homomorphic image of its injective hull, and these rings are termed strongly dual Kasch.
  • Article
    Citation - WoS: 2
    Citation - Scopus: 2
    On simple-injective modules
    (World Scientific Publishing, 2022) Alagöz, Yusuf; Benli Göral, Sinem; Büyükaşık, Engin
    For a right module M, we prove that M is simple-injective if and only if M is min-N-injective for every cyclic right module N. The rings whose simple-injective right modules are injective are exactly the right Artinian rings. A right Noetherian ring is right Artinian if and only if every cyclic simple-injective right module is injective. The ring is QF if and only if simple-injective right modules are projective. For a commutative Noetherian ring R, we prove that every finitely generated simple-injective R-module is projective if and only if R = A × B, where A is QF and B is hereditary. An abelian group is simple-injective if and only if its torsion part is injective. We show that the notions of simple-injective, strongly simple-injective, soc-injective and strongly soc-injective coincide over the ring of integers.
  • Article
    Citation - WoS: 5
    Citation - Scopus: 5
    On simple-direct modules
    (Taylor and Francis Ltd., 2021) Büyükaşık, Engin; Demir, Özlem; Diril, Müge
    Recently, in a series of papers “simple” versions of direct-injective and direct-projective modules have been investigated. These modules are termed as “simple-direct-injective” and “simple-direct-projective,” respectively. In this paper, we give a complete characterization of the aforementioned modules over the ring of integers and over semilocal rings. The ring is semilocal if and only if every right module with zero Jacobson radical is simple-direct-projective. The rings whose simple-direct-injective right modules are simple-direct-projective are fully characterized. These are exactly the left perfect right H-rings. The rings whose simple-direct-projective right modules are simple-direct-injective are right max-rings. For a commutative Noetherian ring, we prove that simple-direct-projective modules are simple-direct-injective if and only if simple-direct-injective modules are simple-direct-projective if and only if the ring is Artinian. Various closure properties and some classes of modules that are simple-direct-injective (resp. projective) are given. © 2020 Taylor & Francis Group, LLC.
  • Article
    Citation - WoS: 8
    Citation - Scopus: 8
    On the Structure of Modules Defined by Subinjectivity
    (World Scientific Publishing, 2019) Altınay, Ferhat; Büyükaşık, Engin; Durgun, Yılmaz
    The aim of this paper is to present new results and generalize some results about indigent modules. The commutative rings whose simple modules are indigent or injective are fully determined. The rings whose cyclic right modules are indigent are shown to be semisimple Artinian. We give a complete characterization of indigent modules over commutative hereditary Noetherian rings. We show that a reduced module is indigent if and only if it is a Whitehead test module for injectivity over commutative hereditary noetherian rings. Furthermore, Dedekind domains are characterized by test modules for injectivity by subinjectivity.
  • Article
    Rings and Modules Characterized by Opposites of Fp-Injectivity
    (Korean Mathematical Society, 2019) Büyükaşık, Engin; Kafkas Demirci, Gizem
    Let R be a ring with unity. Given modules M-R and N-R, M-R is said to be absolutely N-R-pure if M circle times N -> L circle times N is a monomorphism for every extension L-R of M-R. For a module M-R, the subpurity domain of M-R is defined to be the collection of all modules N-R such that M-R is absolutely N-R-pure. Clearly M-R is absolutely F-R-pure for every flat module F-R, and that M-R is FP-injective if the subpurity domain of M is the entire class of left modules. As an opposite of FP-injective modules, M-R is said to be a test for flatness by subpurity (or t.f.b.s. for short) if its subpurity domain is as small as possible, namely, consisting of exactly the flat left modules. Every ring has a right t.f.b.s. module. R-R is t.f.b.s. and every finitely generated right ideal is finitely presented if and only if R is right semihereditary. A domain R is Priifer if and only if R is t.f.b.s. The rings whose simple right modules are t.f.b.s. or injective are completely characterized. Some necessary conditions for the rings whose right modules are t.f.b.s. or injective are obtained.
  • Article
    Citation - WoS: 8
    Citation - Scopus: 9
    Max-Projective Modules
    (World Scientific Publishing, 2020) Alagöz, Yusuf; Büyükaşık, Engin
    Weakening the notion of R-projectivity, a right R-module M is called max-projective provided that each homomorphism f: M ? R/I, where I is any maximal right ideal, factors through the canonical projection : R ? R/I. We study and investigate properties of max-projective modules. Several classes of rings whose injective modules are R-projective (respectively, max-projective) are characterized. For a commutative Noetherian ring R, we prove that injective modules are R-projective if and only if R = A × B, where A is QF and B is a small ring. If R is right hereditary and right Noetherian then, injective right modules are max-projective if and only if R = S × T, where S is a semisimple Artinian and T is a right small ring. If R is right hereditary then, injective right modules are max-projective if and only if each injective simple right module is projective. Over a right perfect ring max-projective modules are projective. We discuss the existence of non-perfect rings whose max-projective right modules are projective. © 2020 World Scientific Publishing Company.
  • Article
    Citation - WoS: 12
    Citation - Scopus: 11
    Rugged Modules: the Opposite of Flatness
    (Taylor and Francis Ltd., 2018) Büyükaşık, Engin; Enochs, Edgar; Rozas, J. R. García; Kafkas Demirci, Gizem; López-Permouth, Sergio; Oyonarte, Luis
    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 all of its modules is a lattice with respect to class inclusion. This lattice, the flatness profile of the ring, allows us, in particular, to focus on modules which have a smallest flatness domain (namely, one consisting of all regular modules.) We establish that such modules exist over arbitrary rings and we call them Rugged Modules. Rings all of whose (cyclic) modules are rugged are shown to be precisely the von Neumann regular rings. We consider rings without a flatness middle class (i.e., rings for which modules must be either flat or rugged.) We obtain that, over a right Noetherian ring every left module is rugged or flat if and only if every right module is poor or injective if and only if R = S×T, where S is semisimple Artinian and T is either Morita equivalent to a right PCI-domain, or T is right Artinian whose Jacobson radical properly contains no nonzero ideals. Character modules serve to bridge results about flatness and injectivity profiles; in particular, connections between rugged and poor modules are explored. If R is a ring whose regular left modules are semisimple, then a right module M is rugged if and only if its character left module M+ is poor. Rugged Abelian groups are fully characterized and shown to coincide precisely with injectively poor and projectively poor Abelian groups. Also, in order to get a feel for the class of rugged modules over an arbitrary ring, we consider the homological ubiquity of rugged modules in the category of all modules in terms of the feasibility of rugged precovers and covers for arbitrary modules.
  • Article
    On pseudo semisimple rings
    (World Scientific Publishing Co. Pte Ltd, 2013) Büyükaşık, Engin; Mohamed, Saad H.; Mutlu, Hatice
    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 and left pseudo semisimple ring is an SSP ring
  • Article
    Citation - WoS: 5
    Citation - Scopus: 3
    Rings Over Which Flat Covers of Simple Modules Are Projective
    (World Scientific Publishing Co. Pte Ltd, 2012) Büyükaşık, Engin
    Let R be a ring with identity. We prove that, the flat cover of any simple right R-module 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 R-module with unique maximal submodule is projective.
  • Article
    Citation - WoS: 13
    Citation - Scopus: 14
    Poor and Pi-Poor Abelian Groups
    (Taylor and Francis Ltd., 2017) Alizade, Rafail; Büyükaşık, Engin
    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 integers. We also prove that pi-poor abelian groups exist. Namely, it is proved that the direct sum of U(ℕ), where U ranges over all nonisomorphic uniform abelian groups, is pi-poor. Moreover, for a pi-poor abelian group M, it is shown that M can not be torsion, and each p-primary component of M is unbounded. Finally, we show that there are pi-poor groups which are not poor, and vise versa.