Results 11 to 20 of about 662 (82)
Cotilting and tilting modules over Prüfer domains
Forum Mathematicum, 2007 The paper fits into the general topic of obtaining structure theorems and classifications of tilting and cotilting modules over certain classes of rings. It contains several important results, and a variety of techniques are employed in order to obtain them.
Silvana Bazzoni
exaly +6 more sources
Partial cotilting modules and the lattices induced by them
Communications in Algebra, 1997 We study a duality between (infinitely generated) cotilting and tilting modules over an arbitrary ring. Dualizing a result of Bongartz, we show that a module P is partial cotilting iff P is a direct summand of a cotilting module C such that the left Ext-orthogonal class ⊥P coincides with ⊥C. As an application, we characterize all cotilting torsion-free
Riccardo Colpi +2 more
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Cosilting complexes and AIR-cotilting modules [PDF]
Journal of Algebra, 2016 25 ...
Peiyu Zhang, Jiaqun Wei
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Cosilting modules arising from cotilting objects [PDF]
, 2021 Let $R$ be a ring. In this paper, we study the characterization of cosilting modules and establish a relation between cosilting modules and cotilting objects in a Grothendieck category. We proved that each cosilting right $R$-module $T$ can be described as a cotilting object in $ [R/I]$, where $I$ is a right ideal of $R$ determined by $T$ and $ [R/I]$
Yonggang Hu, Panyue Zhou
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Relative derived dimensions for cotilting modules [PDF]
Journal of Algebra, 2017 For a Noetherian ring $R$ and a cotilting $R$-module $T$ of injective dimension at least $1$, we prove that the derived dimension of $R$ with respect to the category $\mathcal{X}_T$ is precisely the injective dimension of $T$ by applying Auslander-Buchweitz theory and Ghost Lemma.
Michio Yoshiwaki
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A characterization of n-cotilting and n-tilting modules
Journal of Algebra, 2003 Since its introduction by Brenner-Butler and Happel-Ringel in the 80's, tilting theory has been very useful in the study of Representation Theory of Artin Algebras. In the classical tilting theory, the tilting modules considered are finitely generated and of projective dimension at most one. Generalizations of this concept were given in recent years by
Silvana Bazzoni
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Cotilting modules and Gorenstein homological dimensions [PDF]
The Quarterly Journal of MathematicsABSTRACT For a dualizing module $D$ over a commutative Noetherian ring $R$ with identity, it is known that its Auslander class $\mathscr {A}_D\left(R\right)$ (respectively, Bass class $\mathscr {B}_D\left(R\right)$) is characterized as those $R$-modules with finite Gorenstein flat dimension (respectively, finite Gorenstein injective ...
Kamran Divaani-Aazar +2 more
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All 𝑛-cotilting modules are pure-injective [PDF]
Proceedings of the American Mathematical Society, 2006 We prove that all n n -cotilting R R -modules are pure-injective for any ring R R and any n ≥ 0 n \ge 0 . To achieve this, we prove that ⊥ 1 U ...
Jan Šťovíček
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Comparing four definitions of cotilting modules [PDF]
In contrast to the theory of tilting modules, in the dual theory, there is not a unified definition. However, there are several definitions proposed for cotilting modules. In this paper, we compare four of the main definitions for cotilting modules that have been put forward.
Kamran Divaani-Aazar +2 more
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n-Cotilting and n-tilting modules over ring extensions
Forum Mathematicum, 2005 If \(\Gamma\) is a ring extension of the ring \(R\) (i.e., there is a ring homomorphism \(\xi\colon R\to\Gamma\)), then for every module \(_RV\) we have the induced left \(\Gamma\)-modules \(\Gamma\otimes_RV\) (\(\text{Tor}^R_i(\Gamma,V)\)) and \(\Hom_R(\Gamma,V)\) (\(\text{Ext}^i_R(\Gamma,V)\)).
Alberto Tonolo
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