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Limits of Pure-Injective Cotilting Modules
Algebras and Representation Theory, 2005 Let \(\Lambda\) be an Artin algebra and \(\text{Mod\,}\Lambda\) denotes the category of all right \(\Lambda\)-modules. Infinitely generated cotilting modules in \(\text{Mod\,}\Lambda\) were introduced by \textit{L. Angeleri Hügel} and \textit{F. U. Coelho} [Forum Math. 13, No. 2, 239-250 (2001; Zbl 0984.16009)]. In this paper, the authors study the set
Aslak Bakke Buan, Øyvind Solberg
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Injective Cogenerators, Cotilting Modules and Cosilting Modules
Acta Mathematica Sinica, English Series, 2023The origin of the (co)tilting theory goes back to the work of Bernstein-Gelfand-Ponomarev on reflection functors. Initially focused on finitely generated modules over finite dimensional algebras over a field, it quickly was generalized for other settings (e.g., arbitrary rings, infinitely generated modules).
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Quasi-cotilting modules and hereditary quasi-cotilting modules
Communications in Algebra, 2017 In this paper, we firstly give some basic properties on quasi-cotilting modules. With the help of these properties, we obtain a Quasi-cotilting Theorem (see Theorem 2.8).
Peiyu Zhang, Jiaqun Wei
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FINITISTIC n-SELF-COTILTING MODULES OVER RING EXTENSIONS
JP Journal of Algebra, Number Theory and Applications, 2016 Summary: For a ring \(A\), a ring extension \(B\), and a fixed right \(A\)-module \(M\), we give conditions under which a finitistic \(n\)-self-cotilting module \(M\) extends to a finitistic \(n\)-self-cotilting module \(K=\mathrm{Hom}_A(B,M)\) over the ring extension \(B\). We prove that in case there is a ring homomorphism \(\beta:B\to A\) (hence \(A\
Salah Al-Nofayee
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Gorenstein Cotilting and Tilting Modules
Communications in Algebra, 2015 Auslander and Solberg introduced the concepts of finitely generated cotilting and tilting modules in relative homological algebra considering subfunctors of the Ext-functor. In this article we generalize Auslander–Solberg relative notions by giving the definitions of infinitely generated Gorenstein cotilting and tilting modules by means of Gorenstein ...
Liang Yan, Weiqing Li, Baiyu Ouyang
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t-Structures and cotilting modules over commutative noetherian rings
Mathematische Zeitschrift, 2014 Let \(R\) be a commutative noetherian ring. The authors present a unified approach to several recent classification results over \(R\): -- the classification of compactly generated \(t\)-structures in the unbounded derived category \(\mathcal{D}(R)\) given by \textit{L. Alonso Tarrío} et al. [J. Algebra 324, No.
Lidia Angeleri Hügel, Manuel Saorı́n
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Pure injectivity of n-cotilting modules: the Pr�fer and the countable case
Archiv der Mathematik, 2005 The question as to whether \(n\)-cotilting modules are pure-injective has been studied since 2001 but has only been answered affirmatively in the case of cotilting abelian groups and for 1-cotilting modules over arbitrary rings [\textit{R. Göbel} and \textit{J. Trlifaj}, J. Algebra 224, 110--122 (2000; Zbl 0947.20036); \textit{S. Bazzoni}, Proc.
Silvana Bazzoni +2 more
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A Note on Cotilting Modules and Generalized Morita Duality
, 2004 Given a finitely generated cotilting module over an Artin Algebra, reflexive modules under the action of the contravariant Hom and Ext1 functors are characterized.
Kent R. Fuller +2 more
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Generalizations of n-Tilting and n-Cotilting Modules
Bulletin of the Malaysian Mathematical Sciences Society, 2022 Lixin Mao
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