Mathematics / Matematik
Permanent URI for this collectionhttps://hdl.handle.net/11147/8
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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: 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 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.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: 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: 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.