On module categories with nilpotent infinite radical

Otto Kerner; Andrzej Skowroński

Displaying similar documents to “On module categories with nilpotent infinite radical”

Properties of G-atoms and full Galois covering reduction to stabilizers

Piotr Dowbor (2000)

Colloquium Mathematicae

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Given a group G of k-linear automorphisms of a locally bounded k-category R it is proved that the endomorphism algebra $E n d_{R} (B)$ of a G-atom B is a local semiprimary ring (Theorem 2.9); consequently, the injective $E n d_{R} (B)$ -module ${(E n d_{R} (B))}^{*}$ is indecomposable (Corollary 3.1) and the socle of the tensor product functor $- \otimes_{R} B^{*}$ is simple (Theorem 4.4). The problem when the Galois covering reduction to stabilizers with respect to a set U of periodic G-atoms (defined by the functors $Φ^{U} : ∐_{B \in U} m o d k G_{B} \to m o d (R / G)$ and $Ψ^{U} : m o d (R / G) \to \prod_{B \in U} m o d k G_{B}$ )is full (resp. strictly full)...

On restrictions of generic modules of tame algebras

Raymundo Bautista, Efrén Pérez, Leonardo Salmerón (2013)

Open Mathematics

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Given a convex algebra ∧0 in the tame finite-dimensional basic algebra ∧, over an algebraically closed field, we describe a special type of restriction of the generic ∧-modules.

Functors preserving tameness

J. de la Peña (1991)

Fundamenta Mathematicae

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Full embeddings of almost split sequences over split-by-nilpotent extensions

Ibrahim Assem, Dan Zacharia (1999)

Colloquium Mathematicae

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Let R be a split extension of an artin algebra A by a nilpotent bimodule $_{A} Q_{A}$ , and let M be an indecomposable non-projective A-module. We show that the almost split sequences ending with M in mod A and mod R coincide if and only if $H o m_{A} (Q, τ_{A} M)$ = 0 and $M \otimes_{A} Q = 0$ .

A splitting theorem for multipeak path algebras

Daniel Simson (1991)

Fundamenta Mathematicae

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Trisections of module categories

José A. de la Peña, Idun Reiten (2007)

Colloquium Mathematicae

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Let A be a finite-dimensional algebra over a field k. We discuss the existence of trisections (mod₊ A,mod₀ A,mod₋ A) of the category of finitely generated modules mod A satisfying exactness, standardness, separation and adjustment conditions. Many important classes of algebras admit trisections. We describe a construction of algebras admitting a trisection of their module categories and, in special cases, we describe the structure of the components of the Auslander-Reiten quiver lying...

On Hom-spaces of tame algebras

Raymundo Bautista, Yuriy Drozd, Xiangyong Zeng, Yingbo Zhang (2007)

Open Mathematics

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Let Λ be a finite dimensional algebra over an algebraically closed field k and Λ has tame representation type. In this paper, the structure of Hom-spaces of all pairs of indecomposable Λ-modules having dimension smaller than or equal to a fixed natural number is described, and their dimensions are calculated in terms of a finite number of finitely generated Λ-modules and generic Λ-modules. In particular, such spaces are essentially controlled by those of the corresponding generic modules. ...

Representable equivalences for closed categories of modules

Sonia Dal Pio, Adalberto Orsatti (1994)

Rendiconti del Seminario Matematico della Università di Padova

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Localization of differential operators and of higher order de Rham complexes

Gabriele Vezzosi (1997)

Rendiconti del Seminario Matematico della Università di Padova

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A Morita type theorem for a sort of quotient categories

Simion Breaz (2005)

Czechoslovak Mathematical Journal

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We consider the quotient categories of two categories of modules relative to the Serre classes of modules which are bounded as abelian groups and we prove a Morita type theorem for some equivalences between these quotient categories.