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COTILTING CLASSES OF TORSION-FREE MODULES
Journal of Algebra and Its Applications, 2006A right R-module M is torsion-free (in the sense of Hattori) if [Formula: see text] for all r ∈ R. The class of torsion-free modules is a cotilting class if and only if R is a left p.p.-ring. This paper investigates how the class of torsion-free modules is related to the cotilting classes arising from embeddings of a right (left) non-singular ring R ...
Albrecht, Ulrich, Trlifaj, Jan
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n-COTILTING MODULES AND PURE-INJECTIVITY
Bulletin of the London Mathematical Society, 2004In [J. Algebra 273, No. 1, 359-372 (2004; Zbl 1051.16007)], the author studied generalizations of the definitions of \(1\)-tilting and \(1\)-cotilting for infinitely generated modules over general rings to modules of higher projective dimension. A left \(R\)-module \(C\) is \(n\)-cotilting if (1) \(C\) has injective dimension \(\leq n\), (2) \(\text ...
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Finitisticn-Self-Cotilting Modules
Communications in Algebra, 2009We study a class of modules which can be characterized using a duality theorem, called finitistic n-self-cotilting. Such a module Q can be characterized using dual conditions of some generalizations for star modules: every module M which has a right resolution with n terms isomorphic to finite powers of Q (i.e., M is n-finitely Q-copresented) has a ...
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A NOTE ON TILTING AND COTILTING MODULES
Communications in Algebra, 2005ABSTRACT Let R be an artin algebra. We prove that a tilting R-module ω is cotilting if and only if every finitely generated R-module has finite ω-Gorenstein resolution dimension and that a cotilting R-module ω is tilting if and only if every finitely generated R-module has finite ω-Gorenstein coresolution dimension.
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On tilting and cotilting-type modules.
2005Throughout the paper \(K\) denotes an algebraically closed field and \(A\) is a \(K\)-algebra of finite representation type given by quivers. There are a representation-finite \(K\)-algebra \(A\) of global dimension dimension two, and indecomposable not faithful \(A\)-modules \(T\) and \(U\) with the following properties: (i) \(T\) (resp.\ \(U\)) is a ...
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A characterization of n-cotilting and n-tilting modules
Journal of Algebra, 2004Silvana Bazzoni
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Cotorsion theories induced by tilting and cotilting modules
, 2001 Jan Trlifaj
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*-Modules, co-*-modules and cotilting modules over Noetherian rings
, 1996 Wang Ming-yi, XU Yonghua
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