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Recollements induced by good (co)silting dg-modules

Rongmin Zhu, Jiaqun Wei (2023)

Czechoslovak Mathematical Journal

Let U be a dg- A -module, B the endomorphism dg-algebra of U . We know that if U is a good silting object, then there exist a dg-algebra C and a recollement among the derived categories 𝐃 ( C , d ) of C , 𝐃 ( B , d ) of B and 𝐃 ( A , d ) of A . We investigate the condition under which the induced dg-algebra C is weak nonpositive. In order to deal with both silting and cosilting dg-modules consistently, the notion of weak silting dg-modules is introduced. Thus, similar results for good cosilting dg-modules are obtained. Finally, some...

Relative exact covers

Ladislav Bican, Blas Torrecillas (2001)

Commentationes Mathematicae Universitatis Carolinae

Recently Rim and Teply [11] found a necessary condition for the existence of σ -torsionfree covers with respect to a given hereditary torsion theory for the category R -mod. This condition uses the class of σ -exact modules; i.e. the σ -torsionfree modules for which every its σ -torsionfree homomorphic image is σ -injective. In this note we shall show that the existence of σ -torsionfree covers implies the existence of σ -exact covers, and we shall investigate some sufficient conditions for the converse....

Relative hermitian Morita theory. Part II: Hermitian Morita contexts.

Pieter Verhaeghe, Alain Verschoren (1992)

Publicacions Matemàtiques

We introduce the notion of a relative hermitian Morita context between torsion triples and we show how these induce equivalences between suitable quotient categories of left and right modules.Due to the lack of involutive bimodules, the induced Morita equivalences are not necessarily hermitian, however.

Relative theory in subcategories

Soud Khalifa Mohamed (2009)

Colloquium Mathematicae

We generalize the relative (co)tilting theory of Auslander-Solberg in the category mod Λ of finitely generated left modules over an artin algebra Λ to certain subcategories of mod Λ. We then use the theory (relative (co)tilting theory in subcategories) to generalize one of the main result of Marcos et al. [Comm. Algebra 33 (2005)].

Representations of étale Lie groupoids and modules over Hopf algebroids

Jure Kališnik (2011)

Czechoslovak Mathematical Journal

The classical Serre-Swan's theorem defines an equivalence between the category of vector bundles and the category of finitely generated projective modules over the algebra of continuous functions on some compact Hausdorff topological space. We extend these results to obtain a correspondence between the category of representations of an étale Lie groupoid and the category of modules over its Hopf algebroid that are of finite type and of constant rank. Both of these constructions are functorially...

Rings whose modules are finitely generated over their endomorphism rings

Nguyen Viet Dung, José Luis García (2009)

Colloquium Mathematicae

A module M is called finendo (cofinendo) if M is finitely generated (respectively, finitely cogenerated) over its endomorphism ring. It is proved that if R is any hereditary ring, then the following conditions are equivalent: (a) Every right R-module is finendo; (b) Every left R-module is cofinendo; (c) R is left pure semisimple and every finitely generated indecomposable left R-module is cofinendo; (d) R is left pure semisimple and every finitely generated indecomposable left R-module is finendo;...

Roots of Nakayama and Auslander-Reiten translations

Helmut Lenzing, Andrzej Skowroński (2000)

Colloquium Mathematicae

We discuss the roots of the Nakayama and Auslander-Reiten translations in the derived category of coherent sheaves over a weighted projective line. As an application we derive some new results on the structure of selfinjective algebras of canonical type.

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