Pusat, Dilek
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Pusat, D.
Pusat-Yilmaz, Dilel
Pusat-Yilmaz, Dilek
Pusat, D
Pusat-Yilmaz, Dilel
Pusat-Yilmaz, Dilek
Pusat, D
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Main Affiliation
04.02. Department of Mathematics
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Former Staff
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Documents
9
Citations
79
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5
This researcher does not have a WoS ID.
Scholarly Output
9
Articles
6
Views / Downloads
5493/3104
Supervised MSc Theses
3
Supervised PhD Theses
0
WoS Citation Count
33
Scopus Citation Count
31
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0
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0
WoS Citations per Publication
3.67
Scopus Citations per Publication
3.44
Open Access Source
9
Supervised Theses
3
| Journal | Count |
|---|---|
| Glasgow Mathematical Journal | 2 |
| Communications in Algebra | 1 |
| Comptes Rendus de L'Academie Bulgare des Sciences | 1 |
| Hacettepe Journal of Mathematics and Statistics | 1 |
| Journal of Algebra | 1 |
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9 results
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Now showing 1 - 9 of 9
Master Thesis On δ-perfect and δ-semiperfect rings(Izmir Institute of Technology, 2014) Kızılaslan, Gonca; Pusat, DilekIn this thesis, we give a survey of generalizations of right-perfect, semiperfect and semiregular rings by considering the class of all singular R-modules in place of the class of all R-modules. For a ring R and a right R-module M, a submodule N of M is said to be δ-small in M if, whenever N +X = M with M / X singular, we have X = M. If there exists an epimorphism p : P → M such that P is projective and Ker(p) is δ-small in P, then we say that P is a projective δ-cover of M. A ring R is called δ-perfect (respectively, δ-semiperfect) if every R-module (respectively, simple R-module) has a projective δ-cover. In this thesis, various properties and characterizations of δ-perfect and δ-semiperfect rings are stated.Article Citation - WoS: 8Citation - Scopus: 8Modules Whose Maximal Submodules Are Supplements(Hacettepe Üniversitesi, 2010) Büyükaşık, Engin; Pusat, DilekWe 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 give a complete characterization of the modules whose maximal submodules are supplements over Dedekind domains.Article Citation - WoS: 7Citation - Scopus: 7The Proper Class Generated by Weak Supplements(Taylor and Francis Ltd., 2014) Alizade, Rafail; Demirci, Yılmaz Mehmet; Durğun, Yılmaz; Pusat, DilekWe show that, for hereditary rings, the smallest proper classes containing respectively the classes of short exact sequences determined by small submodules, submodules that have supplements and weak supplement submodules coincide. Moreover, we show that this class can be obtained as a natural extension of the class determined by small submodules. We also study injective, projective, coinjective and coprojective objects of this class. We prove that it is coinjectively generated and its global dimension is at most 1. Finally, we describe this class for Dedekind domains in terms of supplement submodules.Article Completely Cotorsion Modules(Publishing House of the Bulgarian Academy of Sciences, 2012) Pusat, DilekWe show that any finitely generated projective cotorsion left module over a ring of left pure global dimension at most 1 is a direct sum of indecomposable direct summands. We deduce that such a ring is left cotorsion and semiperfect if and only if its left cotorsion envelope is finitely presented. Some extensions of this result are also discussed.Article Citation - WoS: 14Citation - Scopus: 12Injective modules over down-up algebras(Cambridge University Press, 2010) Carvalho, Paula A.A.B.; Lomp, Christian; Pusat, DilekThe purpose of this paper is to study finiteness conditions on injective hulls of simple modules over Noetherian down-up algebras. We will show that the Noetherian down-up algebras A(α, β, γ) which are fully bounded are precisely those which are module-finite over a central subalgebra. We show that injective hulls of simple A(α, β, γ)-modules are locally Artinian provided the roots of X2 − αX − β are distinct roots of unity or both equal to 1.Article Citation - WoS: 3Citation - Scopus: 3Modules Over Prüfer Domains Which Satisfy the Radical Formula(Cambridge University Press, 2007) Buyruk, Dilek; Pusat, DilekIn this paper we prove that if R is a Prüfer domain, then the R-module R ⊕ R satisfies the radical formula. © 2007 Glasgow Mathematical Journal Trust.Article Citation - WoS: 1Citation - Scopus: 1Hereditary Rings With Countably Generated Cotorsion Envelope(Academic Press Inc., 2014) Guil Asensio, Pedro A.; Pusat, DilekLet R be a left hereditary ring. We show that if the left cotorsion envelope C(RR) of R is countably generated, then R is a semilocal ring. In particular, we deduce that C(RR) is finitely generated if and only if R is a semiperfect cotorsion ring. Our proof is based on set theoretical counting arguments. We also discuss some possible extensions of this result.Master Thesis Semiperfect and Perfect Group Rings(Izmir Institute of Technology, 2014) Kalaycı, Tekgül; Pusat, DilekIn this thesis, we give a survey of necessary and sufficient conditions on a group G and a ring R for the group ring RG to be semiperfect and perfect. A ring R is called semiperfect R/RadR is semisimple and idempotents of R/RadR can be lifted to R. It is given that if RG is semiperfect, so is R. Necessary conditions on G for RG to be semiperfect are also given for some special type of groups. For the sufficient conditions, several types of rings and groups are considered. If R is commutative and G is abelian, a complete characterization is given in terms of the polynomial ring R[X]. A ring R is called left (respectively, right) perfect if R/Rad R is semisimple and Rad R is left (respectively, right) T-nilpotent. Equivalently, a ring is called left (respectively, right) perfect if R satisfies the descending chain condition on principal right (respectively, left) ideals. By using these equivalent definitions of a perfect ring and results from group theory, a complete characterization of a perfect group ring RG is given in terms of R and G.Master Thesis Modules Whith Coprimary Decomposition(Izmir Institute of Technology, 2009) Tekin, Semra; Pusat, DilekThis thesis presents the theory of coprimary decomposition of modules over a commutative noetherian ring and its coassociated prime ideals. This theory is first introduced in 1973 by I. G. Macdonald as a dual notion of an important tool of associated primes and primary decomposition in commutative algebra. In this thesis, we studied the basic properties of coassociated prime ideals to a module M and gathered some modules in the literature which have coprimary decomposition. For example, we showed that artinian modules over commutative rings are representable. Moreover if R is a commutative noetherian ring, then we showed that injective modules over R are representable. Finally, we discussed the uniqueness properties of coprimary decomposition.