Results 21 to 30 of about 662 (82)
Abstract elementary classes induced by tilting and cotilting modules have finite character [PDF]
Proceedings of the American Mathematical Society, 2008 This paper continues the study of certain abstract elementary classes (AECs) of modules that was begun in a paper by the author, \textit{J. T. Baldwin} and the reviewer [``\({}^ \perp N\) as an abstract elementary class'', Ann. Pure Appl. Logic 149, No. 1--3, 25--39 (2007; Zbl 1140.03013)].
Jan Trlifaj
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On faithfully balanced modules, F-cotilting and F-Auslander algebras [PDF]
Journal of Algebra, 2019 We revisit faithfully balanced modules. These are faithful modules having the double centralizer property. For finite-dimensional algebras our main tool is the category ${\rm cogen}^1(M)$ of modules with a copresentation by summands of finite sums of $M$ on which ${\rm Hom}(-,M)$ is exact. For a faithfully balanced module $M$ the functor ${\rm Hom}(-,M)
Biao Ma, Julia Sauter
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Journal of Algebra, 2001 A module \(U_R\) is cotilting if \(\text{Cogen}(U_R)=\text{Ker}(\text{Ext}^1_R(-,U_R))\). A cotilting bimodule \(_RU_S\) is a faithfully balanced bimodule which is cotilting on both sides. The contravariant functors \(\Delta_R=\Hom_R(-,U)\) and \(\Gamma_R=\text{Ext}_R(-,U)\) (similarly: \(\Delta_S\) and \(\Gamma_S\)) are considered. A cotilting module \
Francesca Mantese
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Quasi-cotilting modules and torsion-free classes [PDF]
Journal of Algebra and Its Applications, 2018 We prove that all quasi-cotilting modules are pure-injective and cofinendo. It follows that the class [Formula: see text] is always a covering class whenever [Formula: see text] is a quasi-cotilting module. Some characterizations of quasi-cotilting modules are given.
Peiyu Zhang, Jiaqun Wei
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Bimodule monomorphism categories and RSS equivalences via cotilting modules [PDF]
Journal of Algebra, 2018 The monomorphism category $\mathscr{S}(A, M, B)$ induced by a bimodule $_AM_B$ is the subcategory of $ $-mod consisting of $\left[\begin{smallmatrix} X\\ Y\end{smallmatrix}\right]_ $ such that $ : M\otimes_B Y\rightarrow X$ is a monic $A$-map, where $ =\left[\begin{smallmatrix} A&M\\0&B \end{smallmatrix}\right]$.
Bao-Lin Xiong, Pu Zhang, Yuehui Zhang
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Differential graded Koszul duality: An introductory survey
Bulletin of the London Mathematical Society, Volume 55, Issue 4, Page 1551-1640, August 2023., 2023 Abstract This is an overview on derived nonhomogeneous Koszul duality over a field, mostly based on the author's memoir L. Positselski, Memoirs of the American Math. Society 212 (2011), no. 996, vi+133. The paper is intended to serve as a pedagogical introduction and a summary of the covariant duality between DG‐algebras and curved DG‐coalgebras, as ...
Leonid Positselski
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r‐Costar Pair of Contravariant Functors
International Journal of Mathematics and Mathematical Sciences, Volume 2012, Issue 1, 2012., 2012 We generalize r‐costar module to r‐costar pair of contravariant functors between abelian categories.
S. Al-Nofayee, Feng Qi
wiley +1 more source
Torsion pairs and rigid objects in tubes [PDF]
, 2013 We classify the torsion pairs in a tube category and show that they are in bijection with maximal rigid objects in the extension of the tube category containing the Pruefer and adic modules.
A Beligiannis +18 more
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Quotient triangulated categories [PDF]
, 2006 For a self-orthogonal module $T$, the relation between the quotient triangulated category $D^b(A)/K^b({\rm add} T)$ and the stable category of the Frobenius category of $T$-Cohen-Macaulay modules is investigated.
Chen, Xiao-Wu, Zhang, Pu
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Parity sheaves on the affine Grassmannian and the Mirkovi\'c-Vilonen conjecture [PDF]
, 2015 We prove the Mirkovi\'c-Vilonen conjecture: the integral local intersection cohomology groups of spherical Schubert varieties on the affine Grassmannian have no p-torsion, as long as p is outside a certain small and explicitly given set of prime numbers.
Achar, Pramod N., Rider, Laura
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