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.