The Auslander and Ringel–Tachikawa Theorem for Submodule Embeddings

DOI10.1080/00927870903286843zbMath1237.16015arXiv0903.5274OpenAlexW2963617212MaRDI QIDQ3060836

Audrey Moore

Publication date: 10 December 2010

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0903.5274

zbMATH Keywords

direct sumsfinite representation typeArtinian ringsAuslander-Reiten sequencesfull subcategoriescategories of right modulesleft almost split morphismssums of indecomposable modules

Mathematics Subject Classification ID

Module categories in associative algebras (16D90) Representation type (finite, tame, wild, etc.) of associative algebras (16G60) Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers (16G70) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Representations of associative Artinian rings (16G10)

Related Items (9)

Injective objects of monomorphism categories. ⋮ A swiss cheese theorem for linear operators with two invariant subspaces ⋮ Galois covering of pure-semisimple categories ⋮ The ``0, 1-property of exceptional objects for nilpotent operators of degree 6 with one invariant subspace ⋮ Monomorphism categories, cotilting theory, and Gorenstein-projective modules. ⋮ Specifying the Auslander transpose in submodule category and its applications ⋮ Finite direct sums of cyclic embeddings ⋮ Representation-theoretic properties of balanced big Cohen-Macaulay modules ⋮ Monomorphism Operator and Perpendicular Operator

Cites Work

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• An introduction to homological algebra
• An Auslander-type result for Gorenstein-projective modules.
• Auslander-Reiten sequences over Artinian rings
• Almost split sequences in subcategories
• Endomorphism algebras of modules with distinguished partially ordered submodules over commutative rings
• Pure semisimple categories and rings of finite representation type
• Subgroups of Abelian Groups
• Representation Theory of Artin Algebras II
• Posets of infinite prinjective type and embeddings of Kronecker modules into the category of prinjective peakI-spaces
• The Auslander-Reiten translation in submodule categories
• Additive categories of locally finite representation type

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