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Displaying similar documents to “On the relation between maximal rigid objects and τ-tilting modules”

Restriction to Levi subalgebras and generalization of the category 𝒪

Guillaume Tomasini (2013)

Annales de l’institut Fourier

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The category of all modules over a reductive complex Lie algebra is wild, and therefore it is useful to study full subcategories. For instance, Bernstein, Gelfand and Gelfand introduced a category of modules which provides a natural setting for highest weight modules. In this paper, we define a family of categories which generalizes the BGG category, and we classify the simple modules for a subfamily. As a consequence, we show that some of the obtained categories are semisimple. ...

T-Rickart modules

S. Ebrahimi Atani, M. Khoramdel, S. Dolati Pish Hesari (2012)

Colloquium Mathematicae

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We introduce the notions of T-Rickart and strongly T-Rickart modules. We provide several characterizations and investigate properties of each of these concepts. It is shown that R is right Σ-t-extending if and only if every R-module is T-Rickart. Also, every free R-module is T-Rickart if and only if R = Z ₂ ( R R ) ⊕ R ' , where R’ is a hereditary right R-module. Examples illustrating the results are presented.

A family of noetherian rings with their finite length modules under control

Markus Schmidmeier (2002)

Czechoslovak Mathematical Journal

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We investigate the category mod Λ of finite length modules over the ring Λ = A ⊗ k Σ , where Σ is a V-ring, i.e. a ring for which every simple module is injective, k a subfield of its centre and A an elementary k -algebra. Each simple module E j gives rise to a quasiprogenerator P j = A ⊗ E j . By a result of K. Fuller, P j induces a category equivalence from which we deduce that mod Λ ≃ ∐ j b a d h b o x P j . As a consequence we can (1) construct for each elementary k -algebra A over a finite field k a nonartinian noetherian ring Λ such that mod A ≃ mod Λ ,...

An alternate criterion of colocalized-localized modules.

Syed Khalid Nauman (1993)

Extracta Mathematicae

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The aim of this note is to express a module which is localized as well as colocalized in terms of an object of an intersecting subcategory related to static modules.

Estimates of global dimension

Wei Jiaqun (2006)

Czechoslovak Mathematical Journal

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In this note we show that for a * n -module, in particular, an almost n -tilting module, P over a ring R with A = E n d R P such that P A has finite flat dimension, the upper bound of the global dimension of A can be estimated by the global dimension of R and hence generalize the corresponding results in tilting theory and the ones in the theory of * -modules. As an application, we show that for a finitely generated projective module over a VN regular ring R , the global dimension of its endomorphism ring...