Browsing by Author "Agayev, Nazım"
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Abelian Modules
Agayev, Nazım; Harmancı, Abdullah; Halıcıoğlu, Sait; Güngöroğlu, Gonca (Faculty of Mathematics, Physics and Informatics Comenius University, 2009)In this note, we introduce abelian modules as a generalization of abelian rings. Let R be an arbitrary ring with identity. A module M is called abelian if, for any m 2 M and any a 2 R, any idempotent e 2 R, mae = mea. ... 
Central Armendariz Rings
Agayev, Nazım; Güngöroğlu, Gonca; Harmancı, Abdullah; Halıcıoğlu, Sait (Bulletein of the Malaysian Mathematical Sciences Society, 2011)We introduce the notion of central Armendariz rings which are a generalization of Armendariz rings and investigate their properties. We show that the class of central Armendariz rings lies strictly between classes of ... 
Endoprincipally Projective Modules
Üngör, Burcu; Agayev, Nazım; Halıcıoğlu, Sait; Harmancı, Abdullah (Institute of Mathematics, Faculty of Science, University of Novi Sad, 2013)Let R be an arbitrary ring with identity and M a right Rmodule with S = EndR(M). In this paper, we introduce a class of modules that is a generalization of principally projective (or simply p.p.) rings and Baer modules. ... 
Extended Armendariz Rings
Agayev, Nazım; Harmancı, Abdullah; Halıcıoğlu, Sait (Algebras Groups Geom., 2013)In this note we introduce central linear Armendariz rings as a generalization of Armendariz rings and investigate their properties 
On a Class of Semicommutative Modules
Agayev, Nazım; Özen, Tahire; Harmancı, Abdullah (Springer, 2009)Let R be a ring with identity,M a right Rmodule and S = EndR(M). In this note, we introduce Ssemicommutative, SBaer, Sq.Baer and Sp.q.Baer modules. We study the relations between these classes of modules. Also we ... 
On a Class of Semicommutative Rings
Özen, Tahire; Agayev, Nazım; Harmancı, Abdullah (Department of Mathematics, Kyungpook National University, 2011)In this paper, a generalization of the class of semicommutative rings is inves tigated. A ring R is called central semicommutative if for any a; b 2 R, ab = 0 implies arb is a central element of R for each r 2 R. We ... 
On Abelian Rings
Agayev, Nazım; Harmancı, Abdullah; Halıcıoğlu, Sait (TÜBİTAK, 2010)Let α be an endomorphism of an arbitrary ring R with identity. In this note, we introduce the notion of αabelian rings which generalizes abelian rings. We prove that αreduced rings, αsymmetric rings, αsemicommutative ... 
On Principally QuasiBaer Modules
Üngör, Burcu; Agayev, Nazım; Halıcıoğlu, Sait; Harmancı, Abdullah (Aulona Press, 2011)Let R be an arbitrary ring with identity and M a right Rmodule with S = EndR(M). In this paper, we introduce a class of modules that is a generalization of principally quasiBaer rings and Baer modules. The mod ule ... 
On Reduced and Semicommutative Modules
Başer, Muhittin; Agayev, Nazım (TÜBİTAK, 2006)In this paper, various results of reduced and semicommutative rings are extended to reduced and semicommutative modules. In particular, we show: (1) For a principally quasiBaer module, MR is semicommutative if and only ... 
On Rickart Modules
Agayev, Nazım; Halıcıoğlu, Sait; Harmancı, Abdullah (Iranian Mathematical Society, 2012)We investigate some properties of Rickart modules defined by Rizvi and Roman. Let R be an arbitrary ring with identity and M be a right Rmodule with S = EndR(M). A module M is called to be Rickart if for any f 2 S, ... 
On Semicommutative Modules and Rings
Agayev, Nazım; Harmancı, Abdullah (Department of Mathematics at Kyungpook National University, 2007)We say a module MR a semicommutative module if for any m 2 M and any a 2 R, ma = 0 implies mRa = 0. This paper gives various properties of reduced, Armendariz, Baer, QuasiBaer, p:p: and p:q:Baer rings to extend to ... 
On Symmetric Modules
Agayev, Nazım; Halıcıoğlu, Sait; Harmancı, Abdullah (Rivista di Matematica della Università di Parma, 2009)[No Abstract Available]